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Implied liquidity risk premium in the term structure of sovereign credit default swap and bond spreads
Implied liquidity risk premium in the term structure of sovereign credit default swap and bond spreads
Lina El-Jahel2015, The European Journal of Finance
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The Time Varying Properties of Credit and Liquidity Components of CDS Spreads2000 •
Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market
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Using data from the credit default swap (CDS), corporate bond, and equity markets, we construct several measures of liquidity and examine the spill-over of liquidity shocks across these markets. Based on the principal component analysis of multiple liquidity measures, we show that there is a dominant first principal component in each of the markets. However, the linkage of liquidity shocks varies between different markets. In particular, there is a common component between the equity and both CDS and bond markets, but not between the CDS and bond market. Moreover, the vector autoregression results show that while there is spill-over of liquidity shocks between equity and CDS markets, surprisingly there is no clear spill-over of liquidity shocks between equity and bond markets. There appears to be a time lag of liquidity spill-over from the CDS to both bond and equity markets. Finally, we find no evidence of liquidity spill-over from bond to CDS market. Key Words: Liquidity shock; Co...
Journal of Business Economics and Management
The Interactions and Trade-Offs of Sovereign Credit Default Swap (CDS) and Bond Spreads in a Dynamic ContextThis study provides a dynamic analysis of the lead-lag relationship between sovereign Credit Default Swap (CDS) and bond spreads of the highly indebted southern European countries, considering an extensive time sample from the period before the global financial crisis to the latest developments of the sovereign indebtedness in the euro area. We employ an integrated price discovery methodology on a rolling sample, with the intention to shed light on whether the CDS spreads can trigger rises in bond spreads, and the relative efficiency of credit risk pricing in the CDS and bond markets. In addition, we attempt to depict the evolution of the price discovery process regarding the direction of influence from one market to the other. The rolling window analysis verifies that the price discovery process evolves over time, presenting frequent alternations concerning the leading market. We find that during periods of economic turbulence the CDS market leads the bond market in price discovery...
2017 •
The recent global economic downturn that erupted in the mid 2007 saw an increase of the Credit Default Swaps (CDS) by hundred basis points and severe liquidity crunch in the financial sector of the United States. The recession phase highlighted the importance of the liquidity for the investors and underlined the importance of understanding the connection between the liquidity of the market and the credit markets. In depth, this study tries to understand the relation between the liquidity risk in the CDS market and the credit risk. Along the same line of this study, a study conducted on the different Swiss and German companies revealed that credit risk is not the direct originator of the liquidity risk, but it created by a negative credit shock. In addition, this paper focuses on the causes that intensified the global crisis of (2007) as well as the macro-prudential policies are highlighted that will prevent a similar type of crisis in the future.
Recent studies suggested that financial markets correlations and volatilities change during crisis periods. This paper presents a practical framework to test the volatility of sovereign credit default market and sovereign bond market indexes during the sovereign crisis period. Furthermore, our research tests the dynamic relationship between the sovereign CDS market evolution and the sovereign bond market, based on a sample of 10 developed Eurozone countries. Then, we integrate the bond debt's sensitivity presented by its maturity, which is a line of research supported by previous studies. Our results show that both markets are sensitive to internal shocks. Moreover, the dynamic relationship between the two markets is more sensitive to negative information than positive information. Finally, maturity significantly affects the sensitivity of sovereign bonds to CDS market evolution. This study contributes to the empirical literature by presenting, to the best of our knowledge, an unprecedented empirical investigation of the sovereign bond maturity effect's sensitivity to the sovereign CDS market evolution.
Abstract Using data from the credit default swap (CDS), corporate bond, and equity markets, we construct several measures of liquidity and examine the spill-over of liquidity shocks across these markets. Based on the principal component analysis of multiple liquidity measures, we show that there is a dominant first principal component in each of the markets. However, the linkage of liquidity shocks varies between dierent,markets. In particular, there is a common component between the equity and both CDS and bond markets, but not between the CDS and bond market. Moreover, the vector autoregression results show that while there is spill-over of liquidity shocks between equity and CDS markets, surprisingly there is no clear spill-over of liquidity shocks between equity and bond markets. There appears to be a time lag of liquidity spill-over from the CDS to both bond and equity markets. Finally, we find no evidence of liquidity spill-over from bond to CDS market. Key Words: Liquidity sh...
Finance Research Letters
The chicken or the egg? A note on the dynamic interrelation between government bond spreads and credit default swaps2011 •
2017 •
The recent global economic downturn that erupted in the mid 2007 saw an increase of the Credit Default Swaps (CDS) by hundred basis points and severe liquidity crunch in the financial sector of the United States. The recession phase highlighted the importance of the liquidity for the investors and underlined the importance of understanding the connection between the liquidity of the market and the credit markets. In depth, this study tries to understand the relation between the liquidity risk in the CDS market and the credit risk. Along the same line of this study, a study conducted on the different Swiss and German companies revealed that credit risk is not the direct originator of the liquidity risk, but it created by a negative credit shock. In addition, this paper focuses on the causes that intensified the global crisis of (2007) as well as the macro-prudential policies are highlighted that will prevent a similar type of crisis in the future.
■♠♣❧✐❡❞ ▲✐q✉✐❞✐t② ❘✐s❦ Pr❡♠✐✉♠ ✐♥ t❤❡ ❚❡r♠ ❙tr✉❝t✉r❡ ♦❢
❙♦✈❡r❡✐❣♥ ❈r❡❞✐t ❉❡❢❛✉❧t ❙✇❛♣ ❛♥❞ ❇♦♥❞ ❙♣r❡❛❞s
∗
❙❛❛❞ ❇❛❞❛♦✉✐
∗∗
✱ ▲❛r❛ ❈❛t❤❝❛rt
∗∗∗
✱ ▲✐♥❛ ❊❧✲❏❛❤❡❧
❙❡♣t❡♠❜❡r ✷✾✱ ✷✵✶✹
❆❜str❛❝t
■♥ t❤✐s st✉❞②✱ ✇❡ ❢♦❝✉s ♦♥ t❤❡ ❞②♥❛♠✐❝ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ r✐s❦✲♥❡✉tr❛❧ ❧✐q✉✐❞✐t②
r✐s❦ ♣r❡♠✐✉♠ s♣❡❝✐✜❝ t♦ t❤❡ s♦✈❡r❡✐❣♥ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ ✭❈❉❙✮ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✳
❲❡ s❤♦✇ t❤❛t ❧✐q✉✐❞✐t② r✐s❦ ❤❛s ❛ ♥♦♥✲tr✐✈✐❛❧ r♦❧❡ ❛♥❞ ♣❛rt✐❝✐♣❛t❡s ❞✐r❡❝t❧② t♦ t❤❡
✈❛r✐❛t✐♦♥ ♦✈❡r t✐♠❡ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞ s♣r❡❛❞s ❢♦r
❜♦t❤ t❤❡ ♣r❡✲ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s✳ ❙❡❝♦♥❞❧②✱ ♦✉r r❡s✉❧ts ✐♥❞✐❝❛t❡ t❤❛t t❤❡ t✐♠❡✲
✈❛r②✐♥❣ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ♠♦✈❡ ✐♥ ♦♣♣♦s✐t❡ ❞✐r❡❝t✐♦♥s ✇❤✐❝❤
✐♠♣❧② t❤❛t ✇❤❡♥ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❤✐❣❤✱ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❧♦✇ ✭❛♥❞ ✈✐❝❡
✈❡rs❛✮✱ ✇❤✐❝❤ ♠❛② ✐♥ t✉r♥ ❜❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ s✉❜st✐t✉t✐♦♥ ❡✛❡❝t ❜❡t✇❡❡♥ ❈❉❙
❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✳ ❋✐♥❛❧❧②✱ ♦✉r ●r❛♥❣❡r ❝❛✉s❛❧✐t② ❛♥❛❧②s✐s r❡✈❡❛❧s t❤❛t✱ ❛❧t❤♦✉❣❤
t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❛r❡ s✉❜st❛♥t✐❛❧❧② ❞✐✛❡r❡♥t✱ t❤❡r❡ ✐s ❛
str♦♥❣ ❧✐q✉✐❞✐t② ✢♦✇ ❜❡t✇❡❡♥ t❤❡ ❈❉❙ ❛♥❞ t❤❡ ❜♦♥❞ ♠❛r❦❡ts✱ ❤♦✇❡✈❡r ♥♦ ♠❛r❦❡t
s❡❡♠s t♦ ❝♦♥s✐st❡♥t❧② ❧❡❛❞ t❤❡ ♦t❤❡r✳
❏❊▲ ❈❧❛ss✐✜❝❛t✐♦♥s✿ ●✵✵✱ ●✶✷✱ ●✶✸✳
❑❡②✇♦r❞s✿ ❚❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣s✱ ▼❛①✐♠✉♠ ❧✐❦❡❧✐✲
❤♦♦❞✱ ❑❛❧♠❛♥ ✜❧t❡r✱ ❘✐s❦ ♥❡✉tr❛❧ ♠❡❛s✉r❡ ❛♥❞ ▲✐q✉✐❞✐t② r✐s❦✳
✯❊❞❤❡❝ ❇✉s✐♥❡ss ❙❝❤♦♦❧✱ ✸✾✸ Pr♦♠❡♥❛❞❡ ❞❡s ❆♥❣❧❛✐s✱ ❇P ✸✶✶✻✱ ✵✻✷✵✷ ◆✐❝❡ ❈❡❞❡① ✸✱ ❋r❛♥❝❡✳
❡♠❛✐❧✿ s❛❛❞✳❜❛❞❛♦✉✐❅❡❞❤❡❝✲r✐s❦✳❝♦♠✳ ✯✯■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡ ❇✉s✐♥❡ss ❙❝❤♦♦❧✱ ■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡
▲♦♥❞♦♥✱ ❙♦✉t❤ ❑❡♥s✐♥❣t♦♥ ❈❛♠♣✉s✱ ❙❲✼ ✷❆❩ ❯♥✐t❡❞ ❑✐♥❣❞♦♠✳ ❚❡❧✿ ✹✹ ✭✵✮✷✵ ✼✺✾✹ ✾✶✷✻✳ ✱
❡♠❛✐❧✿ ❧✳❝❛t❤❝❛rt❅✐♠♣❡r✐❛❧✳❛❝✳✉❦✳ ✯✯✯ ❚❤❡ ❇✉s✐♥❡ss ❙❝❤♦♦❧✱ ❯♥✐✈❡rs✐t② ♦❢ ❆✉❝❦❧❛♥❞✱
❆✉❝❦❧❛♥❞ ✶✶✹✷✱ ◆❡✇ ❩❡❛❧❛♥❞✳ ❡♠❛✐❧✿ ❧✳❡❧❥❛❤❡❧❅❛✉❝❦❧❛♥❞✳❛❝✳♥③✳
✶
✶ ■♥tr♦❞✉❝t✐♦♥✿
❯♥❞❡rst❛♥❞✐♥❣ t❤❡ ❞②♥❛♠✐❝s ♦❢ s♦✈❡r❡✐❣♥ ❜♦♥❞ ❛♥❞ ✐♥ ♣❛rt✐❝✉❧❛r ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ ✭❈❉❙✮
s♣r❡❛❞s ✐s ❜❡❝♦♠✐♥❣ ✐♥❝r❡❛s✐♥❣❧② ✐♠♣♦rt❛♥t ♥♦t ♦♥❧② ❢♦r ♣r❛❝t✐t✐♦♥❡rs ❜✉t ❛❧s♦ ❢♦r ♣♦❧✐❝② ♠❛❦✲
❡rs✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ ❇■❙ q✉❛rt❡r❧② ❘❡✈✐❡✇ ✭❉❡❝❡♠❜❡r ✷✵✶✵✮ ❛♣♣r♦①✐♠❛t❡❧② ✽✵✪ ♦❢ t❤❡ ❈❉❙
♠❛r❦❡t r❡❧❛t❡s t♦ ❝♦r♣♦r❛t❡ ✐ss✉❡rs ❛♥❞ ✷✵✪ t♦ s♦✈❡r❡✐❣♥ ❡♥t✐t✐❡s✳ ❍♦✇❡✈❡r t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙
♠❛r❦❡t ❤❛s r❡❝♦r❞❡❞ t❤❡ str♦♥❣❡st ❣r♦✇t❤ t❤❡s❡ r❡❝❡♥t ②❡❛rs s❤♦✇✐♥❣ ✺✵✪ ✐♥❝r❡❛s❡ ✐♥ ❣r♦ss
♣♦s✐t✐♦♥s ✭❢r♦♠ ✷✵✵✾ t♦ ✷✵✶✵✮✳ ❯♥❧✐❦❡ t❤❡ ❝♦r♣♦r❛t❡ ❈❉❙ ♠❛r❦❡t ✇❤❡r❡ t❤❡r❡ ✐s ❛ s✐❣♥✐✜❝❛♥t
tr❛❞✐♥❣ ❛❝t✐✈✐t② ❛t t❤❡ ✜✈❡ ②❡❛r ♣♦✐♥t ♦♥❧②✱ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ ♠❛r❦❡t ✐s r❡❧❛t✐✈❡❧② ♠♦r❡ ❧✐q✲
✉✐❞ ❛t ❞✐✛❡r❡♥t ♠❛t✉r✐t✐❡s ✇❤✐❝❤ ♣r♦✈✐❞❡ ✉s ✇✐t❤ ❛ r✐❝❤ s❡t ♦❢ t✐♠❡✲s❡r✐❡s ❛♥❞ ❝r♦ss✲s❡❝t✐♦♥❛❧
✐♥❢♦r♠❛t✐♦♥✳
■♥ t❤✐s st✉❞②✱ ✇❡ ❡①t❡♥❞ t❤❡ ✇♦r❦ ♦❢ ❈❤❡♥✱ ❋❛❜♦③③✐✱ ❛♥❞ ❙✈❡r❞❧♦✈❡ ✭✷✵✶✵✮ ❛♥❞ ❛♥❛❧②s❡ t❤❡
❡✛❡❝t ♦❢ ❧✐q✉✐❞✐t② r✐s❦ ✐♥ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞ s♣r❡❛❞s✳ ❲❡ ❞✐✛❡r❡♥✲
t✐❛t❡ ♦✉rs❡❧✈❡s ❢r♦♠ t❤❡ ♣r❡✈✐♦✉s ❛✉t❤♦rs ❜② ✉s✐♥❣ t❤❡ ✇❤♦❧❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙
❛♥❞ ❜♦♥❞ s♣r❡❛❞s ✇❤✐❧❡ t❤❡② ✇♦r❦ ♦♥ ❛ ❞❛t❛s❡t t❤❛t ❝♦♥t❛✐♥s ♠♦st❧② ✺ ②❡❛r ❝♦r♣♦r❛t❡ ❈❉❙s
❛♥❞ ❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t✐❡s ❝❧♦s❡ t♦ ✜✈❡ ②❡❛r✳ ❇② ✉s✐♥❣ t❤❡ ✐♥❢♦r♠❛t✐♦♥ ❡♠❜❡❞❞❡❞ ✐♥ t❤❡ t✐♠❡✲
s❡r✐❡s ❛♥❞ ❝r♦ss s❡❝t✐♦♥✱ ✇❡ ❣❡t ♠♦r❡ ❛❝❝✉r❛t❡ ♠❡❛s✉r❡ ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✐♥ ❜♦t❤
❜♦♥❞ ❛♥❞ ❈❉❙ ♠❛r❦❡ts✳ ❋✉rt❤❡r♠♦r❡✱ ❜❡❝❛✉s❡ ♦❢ ❞❛t❛ ❛✈❛✐❧❛❜✐❧✐t② ✐ss✉❡s✱ t❤❡ ❛❜♦✈❡✲♠❡♥t✐♦♥❡❞
❛✉t❤♦rs ❝♦♥s✐❞❡r t❤❛t ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❛r❡ ❡q✉❛❧ ❛♥❞ ✉s❡ t❤❛t ❛ss✉♠♣t✐♦♥ t♦ ❡st✐✲
♠❛t❡ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ♦❢ ❜♦t❤ ❜♦♥❞s ❛♥❞ ❈❉❙s✳ ■♥ ❢❛❝t✱ t❤❡✐r ♠❡t❤♦❞ ♠❛② ♥♦t ❣✐✈❡
❛ ❣♦♦❞ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❧✐q✉✐❞✐t② ❢r✐❝t✐♦♥s s♣❡❝✐✜❝ t♦ t❤❡ ❜♦♥❞ ♠❛r❦❡t ❜❡❝❛✉s❡✱ ❛s ✇❡ ✇✐❧❧
s❤♦✇ ❧❛t❡r✱ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❞✐✛❡r❡♥t ❢r♦♠ t❤❛t ♦❢ t❤❡ ❜♦♥❞✳ ■♥ t❤✐s st✉❞② ✇❡ r❡❧❛① s✉❝❤
❛ss✉♠♣t✐♦♥ ❜② ✉s✐♥❣ ❛ s❡♣❛r❛t❡ ❧✐q✉✐❞✐t② ❢❛❝t♦r ❢♦r ❡❛❝❤ ♦❢ t❤❡ s♦✈❡r❡✐❣♥ ❜♦♥❞s ❛♥❞ ❈❉❙s✳
■♥ ♦✉r ♣❛♣❡r✱ ✐♥ ❧✐♥❡ ✇✐t❤ t❤❡ ✜♥❞✐♥❣s ♦❢ ❈❤❡♥✱ ❋❛❜♦③③✐✱ ❛♥❞ ❙✈❡r❞❧♦✈❡ ✭✷✵✶✵✮✱ ✇❡ ❛ss✉♠❡
t❤❛t ✐❧❧✐q✉✐❞✐t② ✭♦r ❧✐q✉✐❞✐t② r✐s❦✮ r❡❞✉❝❡s t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❛ss❡t✳ ❚❤❡ ✐❞❡❛ ✐s t❤❛t ❜♦♥❞ ♣r✐❝❡s
❛♥❞ ❈❉❙ s♣r❡❛❞s tr❛❞❡❞ ✐♥ t❤❡ ♠❛r❦❡t ❝♦♥t❛✐♥ ❧✐q✉✐❞✐t② r✐s❦ ❛♥❞ ❛r❡ t❤✉s ❧❡ss t❤❛♥ t❤❡✐r
❤②♣♦t❤❡t✐❝❛❧ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ ❝♦✉♥t❡r♣❛rts✳ ❆❧t❤♦✉❣❤✱ t❤❡ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ ❜♦♥❞ ♣r✐❝❡s ❛♥❞
❈❉❙ s♣r❡❛❞s ❛r❡ ♥❡✐t❤❡r ♦❜s❡r✈❛❜❧❡ ♥♦r ❡①✐st❡♥t✱ ✇❡ ❦♥♦✇ t❤❛t t❤❡✐r ✈❛❧✉❡s ❝❛♥♥♦t ❜❡ ❤✐❣❤❡r
t❤❛♥ t❤❡✐r ❛s❦ q✉♦t❡s✳ ■❢ ✇❡ ❛ss✉♠❡ t❤❛t ♠✐❞ q✉♦t❡s ❛r❡ ❢❛✐r r❡♣r❡s❡♥t❛t✐♦♥s ♦❢ t❤❡ tr❛❞❡❞
❈❉❙s ❛♥❞ ❜♦♥❞s✱ t❤❡♥ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❛s❦ ❛♥❞ t❤❡ ♠✐❞ q✉♦t❡s ❝♦✉❧❞ r❡♣r❡s❡♥t ❛♥
✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ❢♦r ❜♦t❤ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✶ ✳
❇② ✉s✐♥❣ ❛ s✐♥❣❧❡ ❢❛❝t♦r ♠♦❞❡❧ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ❜♦♥❞ ❛♥❞ ❈❉❙ ♠❛r❦❡t✱ ✇❡ ❡①❛♠✐♥❡ t❤❡
✶
❋♦r ❜♦t❤ ❜♦♥❞s ❛♥❞ ❈❉❙s✱ ✇❡ ❛ss✉♠❡ t❤❛t t❤❡ ♠✐❞ q✉♦t❡ ✐s ♦✉r ❧✐q✉✐❞✐t② r✐s❦ ❜❡♥❝❤♠❛r❦ ❜❡❝❛✉s❡ t❤❡ ♠✐❞
q✉♦t❡ ✐s ❜② ❝♦♥str✉❝t✐♦♥ ❛♥ ❛✈❡r❛❣❡ ♦❢ t❤❡ ❜✐❞ ❛♥❞ t❤❡ ❛s❦ q✉♦t❡s ❛♥❞ t❤✉s ❝♦♥t❛✐♥s ♠♦r❡ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t
❧✐q✉✐❞✐t② r✐s❦ t❤❛♥ t❤❡ ❛s❦ q✉♦t❡ ♦♥❧②✳ ❚❤✉s✱ ❢♦r ✐♥st❛♥❝❡ ❢♦r t❤❡ ❝❛s❡ ♦❢ t❤❡ ❈❉❙ ♠❛r❦❡t✱ ❛❝❝♦r❞✐♥❣ t♦ ♦✉r
♠♦❞❡❧ ❛ss✉♠♣t✐♦♥ ✐❢ t❤❡ ❈❉❙ s♣r❡❛❞ ✐s ❧❡ss ✐❧❧✐q✉✐❞ ✭♠♦r❡ ❧✐q✉✐❞✮ ✐t ✇✐❧❧ ❜❡ ❤✐❣❤❡r t❤❛♥ t❤❡ ❈❉❙ ♠✐❞ q✉♦t❡ ❜✉t
❧♦✇❡r t❤❛♥ t❤❡ ❈❉❙ ❛s❦ q✉♦t❡✳ ❚❤✉s t❤❡ ❛s❦ q✉♦t❡ ✐s t❤❡ ✉♣♣❡r ❜♦✉♥❞ ♦❢ t❤❡ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ ❈❉❙✳
✷
t✐♠❡✲s❡r✐❡s ♣r♦♣❡rt✐❡s ♦❢ t❤❡ r✐s❦✲♥❡✉tr❛❧ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ s♣❡❝✐✜❝ t♦ t❤❡ t❡r♠ str✉❝t✉r❡
♦❢ s♦✈❡r❡✐❣♥ ❜♦♥❞ ❛♥❞ ❈❉❙ s♣r❡❛❞s✳ ❖✉r ❢♦❝✉s ♦♥ t❤❡ ♦♥❡ ❢❛❝t♦r ♠♦❞❡❧ ✐s ♠♦t✐✈❛t❡❞ ❜② t❤❡
❤✐❣❤ ❧❡✈❡❧ ♦❢ ❝♦✲♠♦✈❡♠❡♥ts ❛❝r♦ss ♠❛t✉r✐t✐❡s ❞♦❝✉♠❡♥t❡❞ ✐♥ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞
♠❛r❦❡ts✷ ✳ ❲❡ ❝❤♦♦s❡ t♦ st✉❞② ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✱ t❤r❡❡ ❡♠❡r❣✐♥❣ ❝♦✉♥tr✐❡s ✇✐t❤
❞✐✛❡r❡♥t ❝r❡❞✐t ❤✐st♦r② ❛♥❞ ❢♦r ✇❤✐❝❤ ❛ ❢✉❧❧ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞ s♣r❡❛❞s ✐s
❛✈❛✐❧❛❜❧❡✳ ❇② ❛♣♣❧②✐♥❣ t❤❡ ❑❛❧♠❛♥ ✜❧t❡r✱ ✇❡ s❤♦✇ t❤❛t t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✐s s✐❣♥✐✜❝❛♥t
❢♦r ❜♦t❤ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts ❛♥❞ ✐♥ ❜♦t❤ t❤❡ ♣r❡✲ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s✳
❖✉r ♣❛♣❡r ❝♦♠♣❧❡♠❡♥ts t❤❡ st✉❞② ♦❢ P❛♥ ❛♥❞ ❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮✱ ✐♥ t❤❡ s❡♥s❡ t❤❛t ♦✉r
❝♦♥tr✐❜✉t✐♦♥ s❤❡❞s s♦♠❡ ❧✐❣❤t ♦♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ t❤❛t ♠❛② ❝❛✉s❡ t❤❡ ✈❛r✐❛t✐♦♥ ♦✈❡r✲
t✐♠❡ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙s✸ ✳ ❲❤✐❧❡ P❛♥ ❛♥❞ ❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮ ❡♠♣❤❛s✐③❡ t❤❛t
❛ s✐❣♥✐✜❝❛♥t ♣❛rt ♦❢ t❤❡ ❝♦✲♠♦✈❡♠❡♥t ❛♠♦♥❣ t❤❡ t❡r♠ str✉❝t✉r❡s ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s
✐s tr✐❣❣❡r❡❞ ❜② ❝❤❛♥❣❡s ✐♥ ✐♥✈❡st♦rs ❛♣♣❡t✐t❡s ❢♦r ❝r❡❞✐t ❡①♣♦s✉r❡ ❛t ❛ ❣❧♦❜❛❧ ❧❡✈❡❧✱ r❛t❤❡r
t❤❛♥ ❜② ❛ r❡❛ss❡ss♠❡♥t ♦❢ t❤❡ ❢✉♥❞❛♠❡♥t❛❧ str❡♥❣t❤s ♦❢ t❤❡s❡ s♣❡❝✐✜❝ s♦✈❡r❡✐❣♥ ❡❝♦♥♦♠✐❡s✱
♦✉r r❡s✉❧ts s✉❣❣❡st t❤❛t ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❤❛s ❛ ♥♦♥✲tr✐✈✐❛❧ r♦❧❡ ❛♥❞ ♣❛rt✐❝✐♣❛t❡s ❞✐r❡❝t❧②
t♦ t❤❡ ✈❛r✐❛t✐♦♥ ♦✈❡r t✐♠❡ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s✳ ▼♦r❡♦✈❡r✱ ♦✉r
♣❛♣❡r ❛❧s♦ ❝♦♥tr✐❜✉t❡s t♦ t❤❡ str❡❛♠ ♦❢ t❤❡ ❧✐t❡r❛t✉r❡ t❤❛t ✐♥✈❡st✐❣❛t❡s ✭✐✮ t❤❡ ❧✐♥❦ ❜❡t✇❡❡♥
s♦✈❡r❡✐❣♥ ❜♦♥❞ ❛♥❞ ❈❉❙ ♠❛r❦❡ts ✭❈❛❧✐❝❡✱ ❈❤❡♥✱ ❛♥❞ ❲✐❧❧✐❛♠s ✷✵✶✸❀ ❛♠♦♥❣ ♦t❤❡rs✮✱ ✭✐✐✮ t❤❡
✐♥t❡r❛❝t✐♦♥s ❜❡t✇❡❡♥ ❝r❡❞✐t ❛♥❞ ❧✐q✉✐❞✐t② r✐s❦s ✐♥ t❤❡ s♦✈❡r❡✐❣♥ ❜♦♥❞ ♠❛r❦❡ts ✭▼♦♥❢♦rt ❛♥❞
❘❡♥♥❡ ✷✵✶✶❀ ❇❡❜❡r✱ ❇r❛♥❞t✱ ❛♥❞ ❑❛✈❛❥❡❝③ ✷✵✵✾❀ ❊❥s✐♥❣✱ ●r♦t❤❡✱ ❛♥❞ ●r♦t❤❡ ✷✵✶✷✮ ❛♥❞ ✭✐✐✐✮ t❤❡
t❡r♠ str✉❝t✉r❡ ♦❢ ❜♦♥❞ ♠❛r❦❡t ❧✐q✉✐❞✐t② ✭❙❝❤✉st❡r ❛♥❞ ❯❤r✐❣✲❍♦♠❜✉r❣ ✷✵✶✷❀ ❑❡♠♣❢✱ ❑♦r♥✱ ❛♥❞
❯❤r✐❣✲❍♦♠❜✉r❣ ✷✵✶✷❀ ❛♥❞ ●♦②❡♥❦♦✱ ❙✉❜r❛❤♠❛♥②❛♠✱ ❛♥❞ ❯❦❤♦✈ ✷✵✶✶✮✳ ❲❤✐❧❡ ♠♦st ♣❛♣❡rs
❛♥❛❧②s❡ ❝r❡❞✐t ❛♥❞ ❧✐q✉✐❞✐t② ✐♥t❡r❛❝t✐♦♥s✱ ✐♥ t❤✐s st✉❞② ✇❡ ❢♦❝✉s s♦❧❡❧② ♦♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ t❡r♠
str✉❝t✉r❡ ❢♦r ❡❛❝❤ ♦❢ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✳ ❆❧t❤♦✉❣❤✱ ♦✉r ♠❡t❤♦❞ t♦ ✐s♦❧❛t❡
❝r❡❞✐t r✐s❦ ✐s s✐♠♣❧✐st✐❝✱ ✐t ❡♥❛❜❧❡s ✉s t♦ ❝♦♠♣❛r❡ ❧✐q✉✐❞✐t② r✐s❦ ♦❢ ❈❉❙s ❛♥❞ ❜♦♥❞s ❛t ❝♦♥st❛♥t
♠❛t✉r✐t② ❛♥❞ st✉❞② t❤❡✐r ✐♥t❡r❛❝t✐♦♥s✳ ❋✉rt❤❡r♠♦r❡✱ ❦❡❡♣✐♥❣ t❤❡ ♣r✐❝✐♥❣ ❢r❛♠❡✇♦r❦ s✐♠♣❧❡
✐♥ ♦r❞❡r t♦ ✐♥✈❡st✐❣❛t❡ ❛ ❢❛✐r❧② ♥❡✇ ❛r❡❛ ♦❢ r❡s❡❛r❝❤ ❝♦✉❧❞ ♣r♦✈✐❞❡ ❣♦♦❞ ❡❝♦♥♦♠✐❝ ✐♥t✉✐t✐♦♥
❛♥❞ ✈❛❧✉❛❜❧❡ ✐♥❢♦r♠❛t✐♦♥ ♦♥ ❧✐q✉✐❞✐t② ❝❤❛r❛❝t❡r✐st✐❝s ❢♦r ❢✉rt❤❡r st✉❞✐❡s✳ ❚♦ t❤❡ ❜❡st ♦❢ ♦✉r
❦♥♦✇❧❡❞❣❡✱ t❤✐s ✐s t❤❡ ✜rst ❛tt❡♠♣t t❤❛t ❝♦♠♣❛r❡s ❧✐q✉✐❞✐t② r✐s❦ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞
♠❛r❦❡ts ❜② ✐s♦❧❛t✐♥❣ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❝r❡❞✐t r✐s❦ ❛♥❞ ♠❛t✉r✐t②✳
❖✉r ✜♥❞✐♥❣s ✐♠♣❧② t❤❛t ❛❧t❤♦✉❣❤ t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❛r❡ s✉❜✲
st❛♥t✐❛❧❧② ❞✐✛❡r❡♥t t❤❡r❡ ✐s ❛♥ ✐♠♣♦rt❛♥t ❧✐q✉✐❞✐t② s♣✐❧❧✲♦✈❡r ♦r ❧✐q✉✐❞✐t② ✢♦✇ ❜❡t✇❡❡♥ ❜♦t❤
✷
❋♦r ❡❛❝❤ ♦❢ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡t✱ ♦✉r ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ❛♥❛❧②s✐s ✐♥ ❙❡❝t✐♦♥ ✻ s❤♦✇s t❤❛t ♦♥❡ ❢❛❝t♦r
❝❛♥ ❡①♣❧❛✐♥ ❛ ❧❛r❣❡ ♣❛rt ♦❢ t❤❡ s♣r❡❛❞ ✈❛r✐❛♥❝❡✳
✸
P❛♥ ❛♥❞ ❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮ ❢♦❝✉s ♦♥ t❤❡ ❞②♥❛♠✐❝ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ r✐s❦✲♥❡✉tr❛❧ ❞❡❢❛✉❧t ❛rr✐✈❛❧ r❛t❡ ❛♥❞
r❡❝♦✈❡r② r✐s❦ ✐♥ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s✳
✸
♠❛r❦❡ts✳ ❋✉rt❤❡r♠♦r❡✱ ♦✉r r❡s✉❧ts ✐♥❞✐❝❛t❡ t❤❛t t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ♦❢
❜♦t❤ ❜♦♥❞ ❛♥❞ ❈❉❙ ♠❛r❦❡ts ♠♦✈❡ ✐♥ ♦♣♣♦s✐t❡ ❞✐r❡❝t✐♦♥s ♥❛♠❡❧② ✇❤❡♥ ❧✐q✉✐❞✐t② r✐s❦ ✐♥ t❤❡
❈❉❙ ♠❛r❦❡t ✐s ❤✐❣❤✱ t❤❡ ❜♦♥❞ ♠❛r❦❡t t❡♥❞s t♦ ❤❛✈❡ ❛ ❧♦✇❡r ❧✐q✉❞✐t② r✐s❦ ❛♥❞ ✈✐❝❡ ✈❡rs❛✳ ❙✉❝❤
♦♣♣♦s✐t❡ ♠♦✈❡♠❡♥t ♠❛② ❜❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ s✉❜st✐t✉t✐♦♥ ❡✛❡❝t✳ ❲❤❡♥ t❤❡ ❈❉❙ ♠❛r❦❡t ✐s
✐❧❧✐q✉✐❞✱ ❈❉❙ ❜✉②❡rs r❡q✉✐r❡ ❛ ❞✐s❝♦✉♥t ✐♥ ♦r❞❡r t♦ ❜✉② ❛ ♣r♦t❡❝t✐♦♥✹ ✳ ❍♦✇❡✈❡r✱ ✐❢ t❤❡ ♣r❡♠✐✉♠
r❡q✉✐r❡❞ ✐s t♦♦ ❤✐❣❤✱ ❈❉❙ s❡❧❧❡rs ♠❛② ♣r❡❢❡r t♦ ❜✉② ❝r❡❞✐t r✐s❦ ✐♥ t❤❡ ❜♦♥❞ ♠❛r❦❡t ❜❡❝❛✉s❡ ✐t
❤❛s ❛ ❧♦✇❡r ❧✐q✉✐❞✐t② r✐s❦✳ ❍❡♥❝❡✱ ✐♥✈❡st♦rs tr❛❞❡ ❝r❡❞✐t r✐s❦ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ✐♥
❡❛❝❤ ♠❛r❦❡t✳
❖✉r ♣❛♣❡r ❤❛s ✐♠♣♦rt❛♥t ✐♠♣❧✐❝❛t✐♦♥s ❢♦r r✐s❦ ♠❛♥❛❣❡rs ❛♥❞ ♣♦❧✐❝② ♠❛❦❡rs ❛s ✐t ❡♥❤❛♥❝❡s
♦✉r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ♠♦✈❡♠❡♥ts ❛❧♦♥❣ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❜♦♥❞ ❛♥❞ ❈❉❙
s♣r❡❛❞s✳ ❲❡ ❜❡❧✐❡✈❡ t❤❛t ♦✉r r❡s✉❧ts ❛r❡ ♦❢ ✐♥t❡r❡st t♦ ❛❝❛❞❡♠✐❝s✱ ♣r❛❝t✐t✐♦♥❡rs ❛♥❞ ♦❢ ♣❛rt✐❝✉❧❛r
r❡❧❡✈❛♥❝❡ t♦ ♣♦❧✐❝②♠❛❦❡rs ✐♥ ❢♦r♠✐♥❣ ❛ ❜❡tt❡r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ tr❛♥s♠✐ss✐♦♥ ❝❤❛♥♥❡❧s
❜❡t✇❡❡♥ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ s♦✈❡r❡✐❣♥ ❞❡❜t ♠❛r❦❡ts✳
■♥ ❙❡❝t✐♦♥ ✷✱ ✇❡ ❞✐s❝✉ss t❤❡ r❡❧❛t❡❞ ❧✐t❡r❛t✉r❡✳ ❙❡❝t✐♦♥ ✸ ♣r♦✈✐❞❡s ❛♥ ❡①❛♠♣❧❡ t♦ ✐❧❧✉str❛t❡
❤♦✇ ❧✐q✉✐❞✐t② r✐s❦ r❡❞✉❝❡s t❤❡ ❛ss❡t ✈❛❧✉❡✳ ❙❡❝t✐♦♥ ✹ ✐♥tr♦❞✉❝❡s t❤❡ ❞❛t❛✳ ❙❡❝t✐♦♥ ✺ ❝♦♠♣❛r❡s
❧✐q✉✐❞✐t② r✐s❦ ♦❢ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts ❛t ❝♦♥st❛♥t ♠❛t✉r✐t②✳ ❙❡❝t✐♦♥ ✻ ♣r❡s❡♥ts t❤❡ ♣r✐♥❝✐♣❛❧
❝♦♠♣♦♥❡♥t ❛♥❛❧②s✐s✳ ❙❡❝t✐♦♥ ✼ ❛♥❞ ✽ ✐♥tr♦❞✉❝❡ t❤❡ t❤❡♦r❡t✐❝❛❧ ❢r❛♠❡✇♦r❦✱ t❤❡ ❡st✐♠❛t✐♦♥
♠❡t❤♦❞♦❧♦❣② ❛♥❞ t❤❡ r❡s✉❧ts✳ ❙❡❝t✐♦♥ ✾ ♣r❡s❡♥ts t❤❡ ●r❛♥❣❡r✲❝❛✉s❛❧✐t② ❛♥❛❧②s✐s ❜❡t✇❡❡♥ ❜♦t❤
❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✳ ❋✐♥❛❧❧②✱ ❙❡❝t✐♦♥ ✶✵ ❝♦♥❝❧✉❞❡s✳
✷ ❘❡❧❛t❡❞ ▲✐t❡r❛t✉r❡✿
❚❤❡r❡ ✐s ❛ ❝♦♥s❡♥s✉s ✐♥ t❤❡ ❧✐t❡r❛t✉r❡ t❤❛t ❈❉❙ s♣r❡❛❞s ❛r❡ ✐♥✢✉❡♥❝❡❞ ❜② ♥♦♥✲❞❡❢❛✉❧t ❢❛❝t♦rs
s✉❝❤ ❛s ❧✐q✉✐❞✐t② ❛♥❞ ❝♦rr❡❧❛t✐♦♥ r✐s❦ ✭❈❤❡♥✱ ❋❛❜♦③③✐✱ ❛♥❞ ❙✈❡r❞❧♦✈❡ ✷✵✶✵❀ ❚❛♥❣ ❛♥❞ ❨❛♥
✷✵✵✼❀ ❇♦♥❣❛❡rts✱ ❉❡ ❏♦♥❣✱ ❛♥❞ ❉r✐❡ss❡♥ ✷✵✶✶❀ ❇❛❞❛♦✉✐✱ ❈❛t❤❝❛rt✱ ❛♥❞ ❊❧✲❏❛❤❡❧ ✷✵✶✸❀ ▲✐♥✱
▲✐✉✱ ❲✉ ✷✵✵✾❀ ❇✉❤❧❡r ❛♥❞ ❚r❛♣♣ ✷✵✶✵❀ ❛♠♦♥❣ ♦t❤❡rs✮✳ ❆❧t❤♦✉❣❤ t❤❡ ❧✐t❡r❛t✉r❡ ♦♥ ❈❉❙
❧✐q✉✐❞✐t② ❤❛s s❡❡♥ ❛♥ ✐♠♣♦rt❛♥t ❣r♦✇t❤ ✐♥ t❤❡ ♣❛st ②❡❛rs✱ ❡♠♣✐r✐❝❛❧ st✉❞✐❡s t❤❛t ✐♥✈♦❧✈❡ t❤❡
♠♦❞❡❧✐♥❣ ♦❢ t❤❡ ❡♥t✐r❡ ❈❉❙ ❝✉r✈❡ ✐s st✐❧❧ q✉✐t❡ r❛r❡✳ ❩❤❛♥❣ ✭✷✵✵✽✮ s✉❣❣❡sts ❛ st✉❞② t❤❛t
❡st✐♠❛t❡ ❞❡❢❛✉❧t r✐s❦ ✉s✐♥❣ t❤❡ ❡♥t✐r❡ ❝r❡❞✐t ❝✉r✈❡ ♦❢ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙s ❢♦r t❤❡ ❆r❣❡♥t✐♥❡
❝❛s❡✳ ❚❤❡ ❛✉t❤♦r s✉❣❣❡sts ❛ ♠♦❞❡❧ t❤❛t t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❞②♥❛♠✐❝ ✐♥t❡r❛❝t✐♦♥ ❜❡t✇❡❡♥
✐♥t❡r❡st r❛t❡✱ ❞❡❢❛✉❧t ✐♥t❡♥s✐t②✱ ❡①♣❡❝t❡❞ r❡❝♦✈❡r② r❛t❡ ❛♥❞ ❝♦✉♥t❡r♣❛rt② ❞❡❢❛✉❧t r✐s❦✳ ❍❡ ✜♥❞s
t❤❛t ❞❡❢❛✉❧t r✐s❦ ♣r❡♠✐✉♠ ✐♠♣❧✐❝✐t ✐♥ ❈❉❙ s♣r❡❛❞s ✐s s✉❜st❛♥t✐❛❧✳ ❈❤❡♥✱ ❈❤❡♥❣✱ ❛♥❞ ▲✉✐
✭✷✵✵✽✮ ❡①t❡♥❞ t❤❡ ♠♦❞❡❧ ♦❢ ❈❤❡♥ ❡t ❛❧✳ ✭✷✵✵✽✮ t♦ st✉❞② t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❈❉❙ s♣r❡❛❞s
✹
■♥ ♦✉r ♠♦❞❡❧✱ ✇❡ ❛ss✉♠❡ t❤❛t ❧✐q✉✐❞✐t② r✐s❦ ❡♥t❡rs t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❧❡❣ ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝t ✇❤✐❝❤ ✐♠♣❧✐❡s
t❤❛t ❈❉❙ ❜✉②❡rs ❡❛r♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❜② ❞❡❝r❡❛s✐♥❣ t❤❡ ❛s❦ q✉♦t❡✳
✹
❜② ✉s✐♥❣ ❛ ♠❛tr✐① ♦❢ ❈❉❙ ❞❛t❛s❡t ♣r♦✈✐❞❡❞ ❜② ❏P ▼♦r❣❛♥✳ ❚❤❡② ✜♥❞ t❤❛t t❤❡ ♠♦❞❡❧ ✜ts
✇❡❧❧ t❤❡ ❞❛t❛ ❛♥❞ ❝❛♣t✉r❡s ♠♦st ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❞②♥❛♠✐❝s ❛♥❞ t❤❡ t✐♠❡✲s❡r✐❡s ✈❛r✐❛t✐♦♥✳
❋✉rt❤❡r♠♦r❡✱ t❤❡② ♣r♦✈✐❞❡ ❡✈✐❞❡♥❝❡ ♦❢ ❛ ♥❡❣❛t✐✈❡ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ ❞❡❢❛✉❧t r✐s❦ ❛♥❞ r✐s❦ ❢r❡❡
r❛t❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ ✜♥❞✐♥❣s ♦❢ ❈❤❡♥ ❡t ❛❧✳ ✭✷✵✵✽✮✳ ❈❤❡♥✱ ❈❤❡♥❣✱ ❛♥❞ ❲✉ ✭✷✵✶✶✮ ♣r♦✈✐❞❡
❛ st✉❞② t❤❛t ♣❡r❢♦r♠s ❛ ❥♦✐♥t ❛♥❛❧②s✐s ♦♥ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ✐♥t❡r❡st r❛t❡ ❛♥❞ ❝r❡❞✐t s♣r❡❛❞s
✉s✐♥❣ ❈❉❙ ❞❛t❛✳ ❋✐rst❧②✱ t❤❡② ✜♥❞ t❤❛t t✇♦ ❢❛❝t♦rs ❝❛♥ ♣r✐❝❡ ✇❡❧❧ t❤❡ ✇❤♦❧❡ t❡r♠ str✉❝t✉r❡ ♦❢
t❤❡ ❝r❡❞✐t s♣r❡❛❞s✳ ❙❡❝♦♥❞❧②✱ t❤❡② ❞♦❝✉♠❡♥t t❤❛t ✐♥t❡r❡st r❛t❡ ❢❛❝t♦rs ✐♥✢✉❡♥❝❡ ❜♦t❤ ❝✉rr❡♥t
❛♥❞ ❢✉t✉r❡ ❝❤❛♥❣❡s ♦❢ ❝r❡❞✐t r✐s❦ ❢❛❝t♦rs✳ ❏❛rr♦✇✱ ▲✐✱ ❛♥❞ ❨❡ ✭✷✵✵✾✮ ❡①♣❧♦r❡ t❤❡ ♣♦t❡♥t✐❛❧
❛r❜✐tr❛❣❡ ♦♣♣♦rt✉♥✐t✐❡s ✐♥ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❝♦r♣♦r❛t❡ ❈❉❙ s♣r❡❛❞s✳ ❚❤❡② ❝♦♥str✉❝t ❛
♣♦rt❢♦❧✐♦ ♦❢ ❈❉❙ ❝♦♥tr❛❝ts ✐♥ ♦r❞❡r t♦ t❡st ❢♦r ❛r❜✐tr❛❣❡ ♣r♦✜t❛❜✐❧✐t②✳ ❚❤❡✐r r❡s✉❧ts ❤✐❣❤❧✐❣❤t
t❤❛t t❤❡r❡ ❛r❡ st❛t✐st✐❝❛❧ ❛r❜✐tr❛❣❡ ♦♣♣♦rt✉♥✐t✐❡s t❤❛t ❝♦✉❧❞ ❜❡ ❡①♣❧♦✐t❡❞ ✐♥ t❤❡ t❡r♠ str✉❝t✉r❡
♦❢ t❤❡ ❝♦r♣♦r❛t❡ ❈❉❙ s♣r❡❛❞s✳ ▲♦♥❣st❛✛ ❡t ❛❧✳ ✭✷✵✶✶✮ ✉s❡ s♦✈❡r❡✐❣♥ ❈❉❙ t❡r♠ str✉❝t✉r❡ t♦
❡st✐♠❛t❡ t❤❡ s②st❡♠❛t✐❝ ❞✐str❡ss r✐s❦ ♣r❡♠✐✉♠ ❡♠❜❡❞❞❡❞ ✐♥ t❤❡ ✺ ②❡❛r s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞✳
❚❤❡② ✜♥❞ t❤❛t ♦♥ ❛✈❡r❛❣❡ ❞✐str❡ss r✐s❦ r❡♣r❡s❡♥ts ❛ t❤✐r❞ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s✳ P❛♥
❛♥❞ ❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮ ✐♥✈❡st✐❣❛t❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ❛♥❞ r❡❝♦✈❡r② r❛t❡ ✉s✐♥❣ t❤❡ t❡r♠ str✉❝t✉r❡
♦❢ s♦✈❡r✐❣♥ ❈❉❙ s♣r❡❛❞s ❛♥❞ s❤♦✇ t❤❛t t❤❡ ✜rst ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ❝❛♣t✉r❡s ✾✻✪ ♦❢ t❤❡
✈❛r✐❛t✐♦♥ ♦✈❡r✲t✐♠❡ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡✳ ❚❤❡ ❛✉t❤♦rs ❞❡♠♦♥str❛t❡ t❤❛t ❞✉r✐♥❣ s♦♠❡ s✉❜✲
♣❡r✐♦❞s ❛ s✐❣♥✐✜❝❛♥t ♣❛rt ♦❢ t❤❡ ❝♦✲♠♦✈❡♠❡♥t ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s
❛❝r♦ss ❝♦✉♥tr✐❡s ✐s ❝❛✉s❡❞ ❜② ❝❤❛♥❣❡s ♦❢ ✐♥✈❡st♦rs r✐s❦ ❛♣♣❡t✐t❡ t♦✇❛r❞s ❝r❡❞✐t ❡①♣♦s✉r❡s r❛t❤❡r
t❤❛♥ ❛ r❡❛ss❡ss♠❡♥t ♦❢ t❤❡ ❝r❡❞✐t✇♦rt❤✐♥❡ss ♦❢ s♦✈❡r❡✐❣♥ ❡❝♦♥♦♠✐❡s✳ ❆✉❣✉st✐♥ ✭✷✵✶✷✮ st✉❞② t❤❡
t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s t♦ ✉♥❞❡rst❛♥❞ ❤♦✇ ❣❧♦❜❛❧ ❛♥❞ ❝♦✉♥tr②✲s♣❡❝✐✜❝ r✐s❦
❢❛❝t♦rs ❡①♣❧❛✐♥ t✐♠❡ ✈❛r✐❛t✐♦♥ ✐♥ s♦✈❡r❡✐❣♥ ❝r❡❞✐t r✐s❦✳ ❚❤❡ ❛✉t❤♦r ❛r❣✉❡s t❤❛t t❤❡ s❤❛♣❡ ♦❢
t❤❡ t❡r♠ str✉❝t✉r❡ ❝♦♥✈❡②s s✐❣♥✐✜❝❛♥t ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ r❡❧❛t✐✈❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ❣❧♦❜❛❧ ❛♥❞
❞♦♠❡st✐❝ r✐s❦s✳ ❈♦✉♥tr②✲s♣❡❝✐✜❝ ❢✉♥❞❛♠❡♥t❛❧s ❡①♣❧❛✐♥ r❡❧❛t✐✈❡❧② ♠♦r❡ s♣r❡❛❞ ✈❛r✐❛t✐♦♥ t❤❛♥
❣❧♦❜❛❧ ❢❛❝t♦rs ❛s ❝♦✉♥tr✐❡s ❜❡❝♦♠❡ ♠♦r❡ ❞✐str❡ss❡❞✳ ❍❛♥ ❛♥❞ ❩❤♦✉ ✭✷✵✶✶✮ st✉❞② t❤❡ r❡❧❛t✐♦♥
❜❡t✇❡❡♥ t❤❡ s❧♦♣❡ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❈❉❙ s♣r❡❛❞s✺ ❛♥❞ t❤❡ ❡①♣❡❝t❡❞ st♦❝❦ r❡t✉r♥ ❛♥❞
✜♥❞ t❤❛t t❤❡ s❧♦♣❡ ♣r❡❞✐❝ts t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ r❡t✉r♥s ♦❢ st♦❝❦s ❛♥❞ s✐❣♥❛❧s ❞❡t❡r✐♦r❛t✐♦♥ ✐♥
t❤❡ ✜r♠✬s ❝r❡❞✐t q✉❛❧✐t②✳ ❚r✉❝❦✱ ▲❛✉❜✱ ❛♥❞ ❘❛❝❤❡✈ ✭✷✵✵✹✮ ❡①❛♠✐♥❡ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢
❜♦♥❞ ❛♥❞ ❈❉❙ s♣r❡❛❞s ❢♦r ❞✐✛❡r❡♥t r❛t✐♥❣ ❝❛t❡❣♦r✐❡s✳ ❚❤❡② ❛r❣✉❡ t❤❛t ❛❧t❤♦✉❣❤ ✐♥ t❤❡♦r②
❧♦✇❡r ❝r❡❞✐t q✉❛❧✐t② t❡♥❞s t♦ ❛❝❝♦♠♣❛♥② ❤✐❣❤ ❝r❡❞✐t s♣r❡❛❞s✱ t❤✐s ❡♠♣✐r✐❝❛❧ r❡❧❛t✐♦♥s❤✐♣ ❝❛♥
❜❡ r❛t❤❡r ❝♦♥tr♦✈❡rs✐❛❧ ✇❤❡♥ ✇❡ ♦❜s❡r✈❡ ❜♦♥❞s ✇✐t❤ t❤❡ s❛♠❡ r❛t✐♥❣ ❜✉t ❞✐✛❡r❡♥t ♠❛t✉r✐t✐❡s✳
❚❤❡ ❛✉t❤♦rs ♣r♦✈✐❞❡ ❡✈✐❞❡♥❝❡ t❤❛t t❤❡r❡ ✐s ❛ ♣♦s✐t✐✈❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ♠❛t✉r✐t② ❛♥❞ s♣r❡❛❞s
❢♦r ✐♥✈❡st♠❡♥t ❣r❛❞❡ ❞❡❜t ❛♥❞ t❤✐s ❤♦❧❞s ❢♦r ❜♦t❤ ❜♦♥❞ ❛♥❞ ❈❉❙ s♣r❡❛❞s✳
❚❤❡ ❧✐t❡r❛t✉r❡ r❡✈✐❡✇ ♦♥ t❤❡ ❈❉❙ t❡r♠ str✉❝t✉r❡ ♣r❡s❡♥t❡❞ ❛❜♦✈❡ s❤♦✇s t❤❛t t❤❡r❡ ❛r❡ ❢❡✇
st✉❞✐❡s t❤❛t ❛r❡ ❝❧♦s❡❧② r❡❧❛t❡❞ t♦ ♦✉rs ✇❤✐❝❤ ❛r❡ t❤♦s❡ ♦❢ ❩❤❛♥❣ ✭✷✵✵✽✮✱ P❛♥ ❛♥❞ ❙✐♥❣❧❡t♦♥
✺
❍❛♥ ❛♥❞ ❩❤♦✉ ✭✷✵✶✶✮ ❞❡✜♥❡ t❤❡ s❧♦♣❡ ❛s ❜❡✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ✜✈❡✲②❡❛r ❛♥❞ ♦♥❡✲②❡❛r ❈❉❙ s♣r❡❛❞s✳
✺
✭✷✵✵✽✮ ❛♥❞ ▲♦♥❣st❛✛ ❡t ❛❧✳ ✭✷✵✶✶✮✳ ❆❧❧ ♦❢ t❤❡s❡ st✉❞✐❡s ❡st✐♠❛t❡ ❞❡❢❛✉❧t r✐s❦ ✉s✐♥❣ t❤❡ ❡♥t✐r❡
❝r❡❞✐t ❝✉r✈❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s✳ ❖♥❡ ✐♠♣♦rt❛♥t ❝♦♥tr✐❜✉t✐♦♥ ♦❢ ♦✉r ♣❛♣❡r✱ ❤♦✇❡✈❡r✱ ✐s
t❤❡ ❛♥❛❧②s✐s ♦❢ t❤❡ ❞②♥❛♠✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❧✐q✉✐❞✐t② r✐s❦ ❡♠❜❡❞❞❡❞ ✐♥ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ ❝✉r✈❡✳
❖✉r st✉❞② ✐s ❛❧s♦ ❧✐♥❦❡❞ t♦ t❤❡ ❧✐t❡r❛t✉r❡ t❤❛t ✐♥✈❡st✐❣❛t❡s t❤❡ ✐♥t❡r❛❝t✐♦♥s ❜❡t✇❡❡♥ s♦✈❡r❡✐❣♥
❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✳ ❲❤✐❧❡ ♠❛♥② ♣❛♣❡rs q✉❛♥t✐❢② t❤❡ ❞②♥❛♠✐❝s ♦❢ ❧✐q✉✐❞✐t② ❛♥❞ ❝r❡❞✐t
r✐s❦s ✐♥ t❤❡ ❊✉r♦♣❡❛♥ ❜♦♥❞ ♠❛r❦❡ts ❛♥❞ st✉❞② t❤❡✐r ✐♥t❡r❛❝t✐♦♥s ✭❇❡❜❡r✱ ❇r❛♥❞t✱ ❛♥❞ ❑❛✈❛✲
❥❡❝③ ✷✵✵✾❀ ▼♦♥❢♦rt ❛♥❞ ❘❡♥♥❡ ✷✵✶✶❀ ❈❛❧✐❝❡✱ ❈❤❡♥✱ ❛♥❞ ❲✐❧❧✐❛♠s ✷✵✶✸❀ ❇❛✐✱ ❏✉❧❧✐❛r❞✱ ❛♥❞ ❨✉❛♥
✷✵✶✷❀ P❡❧✐③③♦♥ ❡t ❛❧✳ ✷✵✶✸ ❛♥❞ ♠❛♥② ♦t❤❡rs✮✱ ❤❡r❡ ✇❡ ✇✐❧❧ ♦♥❧② ❢♦❝✉s ♦♥ st✉❞✐❡s t❤❛t ❛♥❛❧②s❡
t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❜♦♥❞ ❧✐q✉✐❞✐t② ❛s t❤❡s❡ ❛r❡ t❤❡ ❝❧♦s❡st t♦ ♦✉r ♣❛♣❡r✳ ❊❥s✐♥❣✱ ●r♦t❤❡✱
❛♥❞ ●r♦t❤❡ ✭✷✵✶✷✮ ❡st✐♠❛t❡ t❤❡ t❡r♠ str✉❝t✉r❡s ♦❢ ❣♦✈❡r♥♠❡♥t✲❣✉❛r❛♥t❡❡❞ ❛❣❡♥❝② ❝✉r✈❡s ❢♦r
●❡r♠❛♥② ❛♥❞ ❋r❛♥❝❡ ✇❤✐❝❤ ❛❧❧♦✇ t❤❡♠ t♦ ♦❜t❛✐♥ r❡❛❧✲t✐♠❡ ❣❛✉❣❡s ♦❢ ❜♦♥❞ ♠❛r❦❡t ❧✐q✉✐❞✐t②
♣r❡♠✐❛ ❢♦r ❛❧❧ ♠❛t✉r✐t✐❡s✳ ❚❤❡② s❤♦✇ t❤❛t ✇❤✐❧❡ t❤❡ s♣r❡❛❞ ❜❡t✇❡❡♥ ❋r❡♥❝❤ ❛♥❞ ●❡r♠❛♥ ❜♦♥❞s
✐♥ ❧❛t❡ ✷✵✵✽✴❡❛r❧② ✷✵✵✾ ✇❛s ✈❡r② ❤✐❣❤✱ ✐t ✇❛s ❡♥t✐r❡❧② ❞✉❡ t♦ ❞✐✛❡r❡♥❝❡s ✐♥ ❧✐q✉✐❞✐t② ♣r❡♠✐❛✳
❆ s♣r❡❛❞ ✐♥❝r❡❛s❡ ♦❢ s✐♠✐❧❛r ♠❛❣♥✐t✉❞❡ ✐♥ ❧❛t❡ ✷✵✶✶ ✇❛s ❛❧s♦ ♣❛rt❧② r❡✢❡❝t✐♥❣ t❤❡ ❞✐✈❡r❣❡♥❝❡
♦❢ ❝r❡❞✐t ♣r❡♠✐❛✳ ❙❝❤✉st❡r ❛♥❞ ❯❤r✐❣✲❍♦♠❜✉r❣ ✭✷✵✶✷✮ ❛♥❛❧②③❡ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ✐❧❧✐q✉✐❞✲
✐t② ♣r❡♠✐❛ ❛s t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ③❡r♦ ❝♦✉♣♦♥ ②✐❡❧❞ ❝✉r✈❡s ♦❢ t✇♦ ❤♦♠♦❣❡♥❡♦✉s ❜♦♥❞
❝❧❛ss❡s t❤❛t ❞✐✛❡r ♦♥❧② ✐♥ t❤❡✐r ❧✐q✉✐❞✐t② ✭✐✳❡✳ ●❡r♠❛♥ ❣♦✈❡r♥♠❡♥t ❜♦♥❞s ❛♥❞ ❜♦♥❞s ♦❢ t❤❡
❑r❡❞✐t❛♥st❛❧t ❢ür ❲✐❡❞❡r❛✉❢❜❛✉ ✭❑❢❲✮ ✇❤✐❝❤ ❛r❡ ❣✉❛r❛♥t❡❡❞ ❜② t❤❡ ●❡r♠❛♥ ❣♦✈❡r♥♠❡♥t✮✳
❚❤❡② s❤♦✇ t❤❛t t❤❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ✐❧❧✐q✉✐❞✐t② ♣r❡♠✐❛ ❞❡♣❡♥❞ str♦♥❣❧②
♦♥ t❤❡ ✜♥❛♥❝✐❛❧ ❛♥❞ ❡❝♦♥♦♠✐❝ s✐t✉❛t✐♦♥✳ ▲♦♥❣st❛✛ ✭✷✵✵✹✮ st✉❞✐❡s ②✐❡❧❞ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥
❚r❡❛s✉r✐❡s ❛♥❞ ❘❡❢❝♦r♣ ❜♦♥❞s✳ ❍❡ ✜♥❞s ❛ ♣♦s✐t✐✈❡ ✐♥✢✉❡♥❝❡ ♦❢ ❝❤❛♥❣❡s ✐♥ t❤❡ ❛♠♦✉♥t ♦❢ ❢✉♥❞s
❤❡❧❞ ✐♥ ♠♦♥❡② ♠❛r❦❡t ♠✉t✉❛❧ ❢✉♥❞s ♦♥ s❤♦rt✲t❡r♠ ✐❧❧✐q✉✐❞✐t② ♣r❡♠✐❛✱ ✇❤❡r❡❛s ♠❡❞✐✉♠✲t❡r♠
♣r❡♠✐❛ ✐♥❝r❡❛s❡s ✇❤❡♥ ❝♦♥s✉♠❡r ❝♦♥✜❞❡♥❝❡ ❞❡❝❧✐♥❡s✳ ❇♦t❤ ❡✛❡❝ts ❝❛♥ ❜❡ ✐♥t❡r♣r❡t❡❞ ✐♥ t❤❡
✇❛② t❤❛t ❛♥ ✐♥❝r❡❛s❡❞ ✇❛r✐♥❡ss t♦ ❜❡❛r r✐s❦ ✐♥❝r❡❛s❡s t❤❡ ♣r❡♠✐✉♠ ♦❢ ❤♦❧❞✐♥❣ ❛♥ ✐❧❧✐q✉✐❞ ❜♦♥❞✳
❑❡♠♣❢✱ ❑♦r♥✱ ❛♥❞ ❯❤r✐❣✲❍♦♠❜✉r❣ ✭✷✵✶✷✮ ❡st✐♠❛t❡ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ✐❧❧✐q✉✐❞✐t② ♣r❡♠✐❛ ❢♦r
●❡r♠❛♥ P❢❛♥❞❜r✐❡❢❡✳ ❚❤❡② ✜♥❞ ❛ ♣♦s✐t✐✈❡ ✐♥✢✉❡♥❝❡ ♦❢ s❤♦rt✲ ❛♥❞ ❧♦♥❣✲t❡r♠ ❧✐q✉✐❞❛t✐♦♥ ♥❡❡❞s
♦♥ t❤❡ r❡s♣❡❝t✐✈❡ ✐❧❧✐q✉✐❞✐t② ♣r❡♠✐❛ ✕ t❤❡ ❢♦r♠❡r ♣r♦①✐❡❞ ❜② ❛ss❡t ♠❛r❦❡t ✈♦❧❛t✐❧✐t✐❡s✱ t❤❡ ❧❛t✲
t❡r ❞✐r❡❝t❧② ❧✐♥❦❡❞ t♦ ❛ ❞❡t❡r✐♦r❛t✐♥❣ ❡❝♦♥♦♠✐❝ ♦✉t❧♦♦❦✳ ●♦②❡♥❦♦✱ ❙✉❜r❛❤♠❛♥②❛♠✱ ❛♥❞ ❯❦❤♦✈
✭✷✵✶✶✮ st✉❞② t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❚r❡❛s✉r② ♠❛r❦❡t ✐❧❧✐q✉✐❞✐t②✳ ❆❧t❤♦✉❣❤ t❤❡✐r ❢♦❝✉s ✐s ♦♥ ❜♦♥❞
♠❛r❦❡t tr❛❞✐♥❣ ❝♦st ♠❡❛s✉r❡❞ ✈✐❛ ❜✐❞ ❛s❦ s♣r❡❛❞s ✐♥st❡❛❞ ♦❢ ②✐❡❧❞ ❞✐✛❡r❡♥t✐❛❧s✱ t❤❡② s❤♦✇ t❤❛t
t❤❡r❡ ✐s ❛♥ ✐♥❝r❡❛s✐♥❣ ✐❧❧✐q✉✐❞✐t② ✐♥ r❡❝❡ss✐♦♥s ❛❝r♦ss ❛❧❧ ♠❛t✉r✐t✐❡s ✇✐t❤ t❤❡ ✐♥❝r❡❛s❡ ❜❡✐♥❣
❡s♣❡❝✐❛❧❧② ♣r♦♥♦✉♥❝❡❞ ❢♦r s❤♦rt✲t❡r♠ ❜♦♥❞s✳ ❋✐♥❛❧❧②✱ ❙❝❤✉st❡r✱ ❚r❛♣♣✱ ❛♥❞ ❯❤r✐❣✲❍♦♠❜✉r❣
✭✷✵✶✸✮ ❞❡✈❡❧♦♣ ❛ ♣❛rs✐♠♦♥✐♦✉s ❡q✉✐❧✐❜r✐✉♠ ♠♦❞❡❧ t❤❛t ❣❡♥❡r❛t❡s ✢❡①✐❜❧❡ t❡r♠ str✉❝t✉r❡s ♦❢
❧✐q✉✐❞✐t② ♣r❡♠✐❛ ❢♦r ✜♥✐t❡✲♠❛t✉r✐t② ❛ss❡ts✳ ❚❤❡② t❡st t❤❡✐r ♠♦❞❡❧ ♦♥ ❝♦r♣♦r❛t❡ ❜♦♥❞s ❛♥❞ ✜♥❞
t❤❛t t❤❡r❡ ✐s ❛ ❤✉♠♣✲s❤❛♣❡❞ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ tr❛❞✐♥❣ ✈♦❧✉♠❡ ❛♥❞ ♠❛t✉r✐t②✱ ❞❡❝r❡❛s✐♥❣ tr❛❞✐♥❣
✈♦❧✉♠❡ ❛s ❛ss❡ts ❛❣❡✱ ❛ ♠♦♥♦t♦♥♦✉s❧② ✐♥❝r❡❛s✐♥❣ ❧✐q✉✐❞✐t② t❡r♠ str✉❝t✉r❡ ✇❤❡♥ ❛s❦ ♣r✐❝❡s ❛r❡
✻
❝♦♥s✐❞❡r❡❞✱ ❛♥❞ ❛ ❧✐q✉✐❞✐t② t❡r♠ str✉❝t✉r❡ ❢r♦♠ ❜✐❞ ♣r✐❝❡s t❤❛t ❝❛♥ ❜❡ ❞❡❝r❡❛s✐♥❣ ♦r ❯✲s❤❛♣❡❞✳
❖✉r st✉❞② ❞✐st✐♥❣✉✐s❤❡s ✐ts❡❧❢ ❢r♦♠ t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② ❧✐t❡r❛t✉r❡ ❜② st✉❞②✐♥❣ t❤❡ t❡r♠ str✉❝t✉r❡
♦❢ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ❛t ♠❛t✉r✐t✐❡s t❤❛t ❛r❡ ❝❧♦s❡ t♦ t❤♦s❡ ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝ts ✭✐✳❡✳ ✶✱ ✸✱
✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs✮ ❛♥❞ ❜② ❛♥❛❧②s✐♥❣ t❤❡ ✐♥t❡r❛❝t✐♦♥s ❜❡t✇❡❡♥ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❛t
❝♦♥st❛♥t ♠❛t✉r✐t②✳ ❚♦ t❤❡ ❜❡st ♦❢ ♦✉r ❦♥♦✇❧❡❞❣❡✱ ❛❧❧ ♣r❡✈✐♦✉s s♦✈❡r❡✐❣♥ ❜♦♥❞ ❧✐q✉✐❞✐t② t❡r♠
str✉❝t✉r❡ ♣❛♣❡rs ❧❡❛✈❡ ❈❉❙ ❧✐q✉✐❞✐t② ♦✉ts✐❞❡ t❤❡ s❝♦♣❡ ♦❢ t❤❡✐r ❛♥❛❧②s✐s✳ ❋✉rt❤❡r♠♦r❡✱ ✇❤✐❧❡
✐♥ t❤❡♦r② ❜♦t❤ ❜♦♥❞s ❛♥❞ ❈❉❙s s❤❛r❡ t❤❡ s❛♠❡ ❞❡❢❛✉❧t r✐s❦ ❝♦♠♣♦♥❡♥t✱ ✐t ✐s st✐❧❧ ✉♥❝❧❡❛r ❤♦✇
❧✐q✉✐❞✐t② r✐s❦ ♦❢ ❜♦t❤ ✐♥str✉♠❡♥ts ❞✐✛❡rs ❛t ❝♦♥st❛♥t ♠❛t✉r✐t② ❛♥❞ t❤✐s ✐s ✇❤❛t t❤✐s st✉❞② ✐s
tr②✐♥❣ t♦ ❝❧❛r✐❢②✳
■♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s❡❝t✐♦♥✱ ✇❡ ♣r♦✈✐❞❡ ❛♥ ❡①❛♠♣❧❡ t♦ ✐❧❧✉str❛t❡ t❤❡ ♠❛✐♥ ✐❞❡❛ ♦❢ ♦✉r ♣❛♣❡r✳
✸ ❆ ◗✉✐❝❦ ■❧❧✉str❛t✐♦♥✿
❚❤❡ ♣❛♣❡r ♣♦st✉❧❛t❡s t❤❛t ✐❧❧✐q✉✐❞✐t② r❡❞✉❝❡s t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❛ss❡t✳ ❚❤✐s ✐❞❡❛ ❝❛♥ ❜❡ ❝❧❡❛r❧②
✐❧❧✉str❛t❡❞ ✇✐t❤ t❤❡ ❢♦❧❧♦✇✐♥❣ ❡①❛♠♣❧❡s✳
❲❡ ❛ss✉♠❡ VBond t♦ ❜❡ t❤❡ ✈❛❧✉❡ ♦❢ ❛ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ s♦✈❡r❡✐❣♥ ❜♦♥❞ ✭✐✳❡✳ ❢r❡❡ ♦❢ ❧✐q✉✐❞✐t②
r✐s❦✮✳ ❚❤❡ ❢✉❧❧ ❜♦♥❞ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ ❝❛♥ ❜❡ ❡①♣r❡ss❡❞ ❛s ❢♦❧❧♦✇s✿
VBond = c
n
X
Pj Q j + Pn Q n + w
Pt (∆Qt )
✭✶✮
t=0
j=1
✇✐t❤
T
X
Qt = e−h∗t
✭✷✮
∆Qt = Qt−1 − Qt
✭✸✮
❛♥❞
c✱ Pt ✱ Qt ✱ h ❛♥❞ w r❡♣r❡s❡♥t t❤❡ ❝♦✉♣♦♥ r❛t❡✱ t❤❡ r✐s❦✲❢r❡❡ ❞✐s❝♦✉♥t ❢❛❝t♦r✱ t❤❡ s✉r✈✐✈❛❧
♣r♦❜❛❜✐❧✐t②✱ t❤❡ ❤❛③❛r❞ r❛t❡ ❢❛❝t♦r ❛♥❞ t❤❡ r❡❝♦✈❡r② r❛t❡ r❡s♣❡❝t✐✈❡❧②✳ T ❝♦rr❡s♣♦♥❞s t♦ t❤❡
t✐♠❡ ♦❢ ❞❡❢❛✉❧t ❛♥❞ ∆Qt t♦ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ s✉r✈✐✈✐♥❣ t✐❧❧ t − 1 ❛♥❞ ❞❡❢❛✉❧t✐♥❣ ❜❡t✇❡❡♥ t − 1
❛♥❞ t✳
∗
❲❡ ♥♦✇ ❞❡✜♥❡ VBond
t♦ ❜❡ t❤❡ ✈❛❧✉❡ ♦❢ ❛ ❜♦♥❞ ✇✐t❤ ❧✐q✉✐❞✐t② r✐s❦ ❛♥❞ ✐♥tr♦❞✉❝❡ ❛ ❧✐q✉✐❞✐t②
❞✐s❝♦✉♥t ❢❛❝t♦r ✐♥ t❤❡ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛✳
∗
VBond
=c
n
X
Pj Qj Lbond
j
+
Pn Qn Lbond
n
+
T
X
t=0
j=1
✼
Pt (∆Qt )Lbond
t
✭✹✮
✇✐t❤
= e−y
Lbond
t
✭✺✮
bond ∗t
r❡♣r❡s❡♥t✐♥❣ t❤❡ ❧✐q✉✐❞✐t② ❞✐s❝♦✉♥t ❢❛❝t♦r ❛♥❞ y bond ❧✐q✉✐❞✐t② r✐s❦✳
∗
❇❡❝❛✉s❡ ♦❢ t❤❡ ❛❞❞✐t✐♦♥❛❧ ❞✐s❝♦✉♥t ❢❛❝t♦r Lbond
✱ VBond
< VBond ✳ ❚❤❡r❡❢♦r❡ ❧✐q✉✐❞✐t② r✐s❦
t
r❡❞✉❝❡s t❤❡ ❛ss❡t ✈❛❧✉❡✳
❚❤❡ s❛♠❡ ✐❞❡❛ ❝❛♥ ❜❡ ❛♣♣❧✐❡❞ t♦ ❈❉❙s✳
sT (
n
X
Pj Qj ) = (1 − w)
T
X
Pt (∆Qt )
✭✻✮
t=0
j=1
✇❤❡r❡ sT r❡♣r❡s❡♥ts t❤❡ ❈❉❙ s♣r❡❛❞ ✭❢r❡❡ ♦❢ ❧✐q✉✐❞✐t② r✐s❦✮ ♣❛✐❞ ♦♥ ❛ s❡♠✐✲❛♥♥✉❛❧ ❜❛s✐s✳ ❚❤❡
P
P
t❡r♠ sT ( nj=1 Pj Qj ) ✐♥ ❡q✉❛t✐♦♥ ✭✻✮ ❝♦rr❡s♣♦♥❞s t♦ ♣r❡♠✐✉♠ ❧❡❣ ❛♥❞ (1 − w) Tt=0 Pt (∆Qt )
t♦ t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❧❡❣✳ ❲❡ ♣♦st✉❧❛t❡ t❤❛t t❤❡ ❈❉❙ s♣r❡❛❞ ✐♥ t❤❡ ♠❛r❦❡t s∗T ❝♦♥t❛✐♥s s♦♠❡
❧✐q✉✐❞✐t② r✐s❦ ❛♥❞ s❤♦✉❧❞ ❜❡ ❧❡ss t❤❛♥ t❤❡ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ s♣r❡❛❞ sT ✳ ❚❤❡r❡❢♦r❡✱
s∗T (
n
X
Pj Qj ) = (1 − w)
Pt (∆Qt )LCDS
t
✭✼✮
t=0
j=1
✇❤❡r❡
T
X
= e−y
LCDS
t
CDS ∗t
✭✽✮
r❡♣r❡s❡♥t✐♥❣ t❤❡ ❧✐q✉✐❞✐t② ❞✐s❝♦✉♥t ❢❛❝t♦r ❛♥❞ y CDS ❧✐q✉✐❞✐t② r✐s❦✳
s∗T < sT ✐s ❥✉st✐✜❡❞ ❜② t❤❡ ❢❛❝t t❤❛t✱ ✐♥ t❤❡♦r②✱ t❤❡ ❈❉❙ ❝♦♥tr❛❝t ❤❛s ❛ ✈❛❧✉❡ ♦❢ ③❡r♦✳ ❚❤✉s✱
t❤❡ ❧✐q✉✐❞✐t② ❞✐s❝♦✉♥t ❢❛❝t♦r LCDS
✐♥tr♦❞✉❝❡❞ ✐♥ t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❧❡❣ ✐♥❞✉❝❡s t❤❡ s♣r❡❛❞s sT t♦
t
∗
❞❡❝r❡❛s❡ t♦ sT ✐♥ ♦r❞❡r t♦ ❜r✐♥❣ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝t ❜❛❝❦ t♦ ③❡r♦✳ ❆ss✉♠✐♥❣ t❤❛t
LCDS
❡♥t❡rs t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❧❡❣ ✐♠♣❧✐❡s t❤❛t ❈❉❙ ❜✉②❡rs ❡❛r♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❜②
t
❞❡❝r❡❛s✐♥❣ t❤❡ ❛s❦ q✉♦t❡✳
■t ✐s ✐♠♣♦rt❛♥t t♦ ♥♦t❡ t❤❛t LCDS
6= Lbond
✇❤✐❝❤ ✐♥❞✐❝❛t❡ t❤❛t t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ❞✐s❝♦✉♥t
t
t
❢❛❝t♦r ✐♥tr♦❞✉❝❡❞ ❢♦r ❈❉❙s ✐s ❞✐✛❡r❡♥t ❢r♦♠ t❤❛t ♦❢ t❤❡ ❜♦♥❞s✳
■♥ ✇❤❛t ❢♦❧❧♦✇s✱ ✇❡ ❞❡s❝r✐❜❡ ♦✉r ❞❛t❛s❡t✳
✹ ❉❛t❛ ❉❡s❝r✐♣t✐♦♥✿
❲❡ ❢♦❝✉s ♦♥ ❡♠❡r❣✐♥❣ ♠❛r❦❡t ❝♦✉♥tr✐❡s t♦ r✉♥ ♦✉r ❛♥❛❧②s✐s s✐♥❝❡ t❤❡✐r s♦✈❡r❡✐❣♥ ❞❡❜t ✐s
tr❛❞❡❞ ✐♥ ❯❙ ❞♦❧❧❛r✱ t❤✐s ❛✈♦✐❞s ❛♥② ❝✉rr❡♥❝② ♠✐s♠❛t❝❤ ✇✐t❤ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ ❝✉rr❡♥❝②✳ ❖✉r
❞❛t❛ s♣❛♥s ❢r♦♠ ◆♦✈❡♠❜❡r ✷✵✵✺ t♦ ❙❡♣t❡♠❜❡r ✷✵✶✵✳ ❋♦r t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ t❤❡ ❞❡❢❛✉❧t
✽
❢r❡❡ ✐♥t❡r❡st r❛t❡✱ ✇❡ ❢♦❧❧♦✇ t❤❡ ❛♣♣r♦❛❝❤ ♦❢ ▲♦♥❣st❛✛✱ ▼✐t❤❛❧✱ ❛♥❞ ◆❡✐s ✭✷✵✵✺✮ ❛♥❞ P❛♥ ❛♥❞
❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮ ❛♥❞ ✉s❡ t❤❡ ❚r❡❛s✉r② ❈✉r✈❡ ❝♦♠♠♦♥❧② ❦♥♦✇♥ ❛s ❈▼❚✳ ❲❡ ❝♦❧❧❡❝t t❤❡ ❞❛t❛
♦♥ ❛ ❞❛✐❧② ❜❛s✐s ❢r♦♠ t❤❡ ❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❍✳✶✺ st❛t✐st✐❝❛❧ r❡❧❡❛s❡ ❢♦r t❤❡ ❝♦♥st❛♥t ♠❛t✉r✐t②
s✐①✲♠♦♥t❤✱ ♦♥❡✱ t✇♦✱ t❤r❡❡✱ ✜✈❡✱ s❡✈❡♥✱ t❡♥✱ t✇❡♥t② ❛♥❞ t❤✐rt② ②❡❛r r❛t❡s✳ ❲❡ t❤❡♥ ✉s❡ t❤❡
❝✉❜✐❝ s♣❧✐♥❡ ❛❧❣♦r✐t❤♠ t♦ ✐♥❢❡r t❤❡ ❞✐s❝♦✉♥t ❢❛❝t♦rs ❛t s❡♠✐✲❛♥♥✉❛❧ ✐♥t❡r✈❛❧s✳
❲❡ ❞♦✇♥❧♦❛❞ ❜✐❞✱ ❛s❦ ❛♥❞ ♠✐❞ q✉♦t❡s ❢♦r t❤❡ ✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs ❈❉❙ s♣r❡❛❞s ♦♥ ❛ ❞❛✐❧②
❜❛s✐s ❢r♦♠ ❉❛t❛str❡❛♠ ❘❡✉t❡rs ❢♦r t❤❡ ❢♦❧❧♦✇✐♥❣ ❝♦✉♥tr✐❡s✿ ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✳
❚❤❡s❡ ❝♦✉♥tr✐❡s ❤❛✈❡ ❞✐✛❡r❡♥t ❣❡♦♣♦❧✐t✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ❛♥❞ ❤❛✈❡ ❛ r✐❝❤ s❡t ♦❢ s♦✈❡r❡✐❣♥
❜♦♥❞s ✇❤✐❝❤ ❡♥❛❜❧❡ ✉s t♦ st✉❞② t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r♦♣❡rt✐❡s ♦❢ t❤❡✐r s♦✈❡r❡✐❣♥ ❜♦♥❞ ♠❛r❦❡ts✳
❆♥♦t❤❡r ♣❛rt✐❝✉❧❛r ❢❡❛t✉r❡ ♦❢ t❤♦s❡ ❝♦✉♥tr✐❡s ✐s t❤❡ ❛✈❛✐❧❛❜✐❧✐t② ♦❢ ❛ r✐❝❤ s❡t ♦❢ ❜♦♥❞s ✇✐t❤
❞✐✛❡r❡♥t ♠❛t✉r✐t✐❡s ✇❤✐❝❤ ✇✐❧❧ ❡♥❛❜❧❡ ✉s t♦ ✧❜r❛❝❦❡t✧ t❤❡ ♠❛t✉r✐t✐❡s ♦❢ t❤❡ ❈❉❙s ✭❈❢ ❙❡❝t✐♦♥
✺✳✸✮✳
❲❡ ♦❜t❛✐♥ t❤❡ ❜♦♥❞ ❞❛t❛ ♦♥ ❛ ❞❛✐❧② ❜❛s✐s ❢r♦♠ ❉❛t❛str❡❛♠✳ ❲❡ ❝♦❧❧❡❝t t❤❡ ❜✐❞✱ ❛s❦ ❛♥❞
♠✐❞ ♣r✐❝❡s ❢♦r ❡❛❝❤ ❞♦❧❧❛r ❞❡♥♦♠✐♥❛t❡❞ ❜♦♥❞ ✐ss✉❡❞ ❜② t❤❡ r❡❧❡✈❛♥t ❝♦✉♥tr② ❛♥❞ ❢♦❝✉s ♦♥❧② ♦♥
✜①❡❞ ❝♦✉♣♦♥ ❜♦♥❞s ✇✐t❤ ♥♦ ♦♣t✐♦♥ ❡♠❜❡❞❞❡❞✳ ❚❤❡ ❜✐❞✴❛s❦ ❛r❡ ■❈▼❆ ❞❛t❛✱ t❤❡s❡ ❛r❡ q✉♦t❡s
♣r♦✈✐❞❡❞ ❜② ✸✵ ✐♥✈❡st♠❡♥t ❜❛♥❦s✳ ❆t t❤❡ ❡♥❞ ♦❢ ❡❛❝❤ ✇♦r❦✐♥❣ ❞❛②✱ t❤❡✐r ❝❧♦s✐♥❣ ❜✐❞ ❛♥❞ ❛s❦
q✉♦t❡s ❛r❡ s❡♥t t♦ ❳tr❛❦t❡r ✇❤❡r❡ t❤❡② ❛r❡ ✈❛❧✐❞❛t❡❞ ❛♥❞ ♣r♦❝❡ss❡❞ t♦ ♣r♦✈✐❞❡ ❛♥ ❛✈❡r❛❣❡ ❜✐❞
❛♥❞ ❛s❦ ❢♦r ❡❛❝❤ s❡❝✉r✐t②✳
■♥ ♦✉r ✐♠♣❧❡♠❡♥t❛t✐♦♥ ✇❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ t❤❡ ❜✐❞✱ ❛s❦ ❛♥❞ ♠✐❞ ②✐❡❧❞s✳ ❙✐♥❝❡ t❤❡② ❛r❡ ♥♦t
❞✐r❡❝t❧② ❞♦✇♥❧♦❛❞❛❜❧❡✱ ✇❡ ♥❡❡❞ t♦ ❝♦♠♣✉t❡ t❤❡♠ ✐♥ ♦r❞❡r t♦ ❝♦♠♣❛r❡ t❤❡ ②✐❡❧❞ s♣r❡❛❞s ✇✐t❤
t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s✳
❙♦✈❡r❡✐❣♥ ❜♦♥❞s ❛r❡ s❡♠✐✲❛♥♥✉❛❧ ❝♦✉♣♦♥ ❜♦♥❞s ✇❤✐❝❤ ♠❡❛♥s t❤❛t ❢♦r ❛ ❜♦♥❞ ♣r✐❝❡ CBt (C, N, τ )✱
t❤❡ ❛♥♥✉❛❧ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② xt ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ✇❛②✿
CBt (C,N,τ )=
PN
i=1
c
xt
xt
(1 + )−(τ +0.5(i−1)) + F ∗ (1 + )−(τ +0.5(N −1))
2
2
2
✭✾✮
✇❤❡r❡ c ✐s t❤❡ ❛♥♥✉❛❧ ❝♦✉♣♦♥ r❛t❡✻ ✱ F t❤❡ ❢❛❝❡ ✈❛❧✉❡✱ N t❤❡ ♥✉♠❜❡r ♦❢ r❡♠❛✐♥✐♥❣ ❝♦✉♣♦♥
♣❛②♠❡♥ts ❛♥❞ τ = TT−t t❤❡ r❛t✐♦ ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ❞❛②s ✉♥t✐❧ t❤❡ ♥❡①t ❝♦✉♣♦♥ ♣❛②♠❡♥t t♦ t❤❡
♥✉♠❜❡r ♦❢ ❞❛②s ✐♥ t❤❡ ❝♦✉♣♦♥ ♣❡r✐♦❞✳
■♥ ♦r❞❡r t♦ ❡st✐♠❛t❡ s♦✈❡r❡✐❣♥ ❜♦♥❞ s♣r❡❛❞s✱ ✇❡ ✜rst ♥❡❡❞ t♦ ❡①tr❛❝t t❤❡ r✐s❦✲❢r❡❡ r❛t❡✳
❚❤❡r❡❢♦r❡✱ ❢♦r ❡❛❝❤ ❜♦♥❞ ✇❡ s♦❧✈❡ ❢♦r t❤❡ s②♥t❤❡t✐❝ ❞❡❢❛✉❧t✲❢r❡❡ ❜♦♥❞ ✇✐t❤ ✐❞❡♥t✐❝❛❧ ❝♦✉♣♦♥
❛♥❞ ♠❛t✉r✐t② ❛s t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❜♦♥❞✳ ❚❤✐s ✐s ❞♦♥❡ ✐♥ t✇♦ st❡♣s✳ ❋✐rst ✇❡ ✉s❡ t❤❡ ❞❡❢❛✉❧t
✻
❲❡ ❛ss✉♠❡ t❤❛t t❤❡ ✜rst ❝♦✉♣♦♥ ♣❛②♠❡♥t ♦❝❝✉rs ✐♥ t❤❡ ✜rst s❡tt❧❡♠❡♥t ❞❛t❡ ♦❢ ♦✉r t✐♠❡ s❡r✐❡s✳
✾
❢r❡❡ t❡r♠ str✉❝t✉r❡ ♦❢ ✐♥t❡r❡st r❛t❡ ✭✐✳❡✳ ❚r❡❛s✉r② ❝✉r✈❡✮ t♦ ❝♦♠♣✉t❡ t❤❡ ♣r✐❝❡ ♦❢ ❞❡❢❛✉❧t✲❢r❡❡
❝♦✉♣♦♥ ❜♦♥❞s ❛s t❤❡ s✉♠ ♦❢ ❞✐s❝♦✉♥t❡❞ ③❡r♦ ❝♦✉♣♦♥ r❛t❡s ♠✉❧t✐♣❧✐❡❞ ❜② c/2✱ t❤❡♥ ✇❡ s♦❧✈❡
❢♦r t❤❡ ❞❡❢❛✉❧t✲❢r❡❡ ②✐❡❧❞✳ ❋✐♥❛❧❧②✱ ✇❡ ❝♦♠♣✉t❡ ❜♦♥❞ s♣r❡❛❞s ❜② t❛❦✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥
❞❡❢❛✉❧t❛❜❧❡ ❜♦♥❞ ②✐❡❧❞s ❛♥❞ s②♥t❤❡t✐❝ ❞❡❢❛✉❧t✲❢r❡❡ ❝♦✉♣♦♥ ❜♦♥❞ ②✐❡❧❞s✳ ❚❛❜❧❡ ✶ ♣r❡s❡♥ts ❛
❞❡s❝r✐♣t✐♦♥ ♦❢ ♦✉r ❜♦♥❞ ❞❛t❛s❡t ✇✐t❤ ✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡ ❛✈❡r❛❣❡ ♠✐❞ ②✐❡❧❞✱ ♠❛t✉r✐t② ❞❛t❡s✱
❝♦✉♣♦♥ ♣❛②♠❡♥t r❛t❡s ❛♥❞ ✐ss✉❡ ❞❛t❡s✳ ❚❤❡ ❞✐✈❡rs✐t② ✐♥ ❜♦♥❞ ♠❛t✉r✐t✐❡s ✇✐❧❧ ❤❡❧♣ ✉s ♠❛t❝❤
❛s ❝❧♦s❡❧② ❛s ♣♦ss✐❜❧❡ t❤❡ ♠❛t✉r✐t✐❡s ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝ts ✭✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs✮✳
■♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s❡❝t✐♦♥✱ ✇❡ ✉s❡ ♦✉r ❞❛t❛s❡t t♦ ❡st✐♠❛t❡ ❧✐q✉✐❞✐t② r✐s❦ ♦❢ ❜♦t❤ ❈❉❙ ❛♥❞
❜♦♥❞ s♣r❡❛❞s✳
✺ ❆ ❘♦✉❣❤ ❊st✐♠❛t✐♦♥ ♦❢ ❇♦♥❞ ❛♥❞ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦✿
■♥ t❤✐s s❡❝t✐♦♥✱ ✇❡ ❛ss✉♠❡ t❤❛t t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② h ❛♥❞ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ y ❞❡✜♥❡❞ ✐♥
❡q✉❛t✐♦♥ ✭✷✮ ❛♥❞ ✭✺✮ ❛r❡ ❝♦♥st❛♥t✼ ✳ ❲❡ t❤❡♥ ♣❡r❢♦r♠ ❛ s✐♠♣❧❡ ❡①❡r❝✐s❡ ✇❤❡r❡ ✇❡ ❡①tr❛❝t ❈❉❙
❧✐q✉✐❞✐t② r✐s❦ ❢r♦♠ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ t❡r♠ str✉❝t✉r❡ ❛♥❞ ❝♦♠♣❛r❡ ✐t ✇✐t❤ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦
✭❡①tr❛❝t❡❞ ❢r♦♠ ❜♦♥❞ ②✐❡❧❞s✮✳
✺✳✶
❈❉❙ ❉✐s❝r❡t✐③❛t✐♦♥✿
❲❡ ✜rst ❝♦♠♣✉t❡ t❤❡ ❞❡❢❛✉❧t ❛♥❞ ❧✐q✉✐❞✐t② ✐♥t❡♥s✐t② h ❛♥❞ y r❡s♣❡❝t✐✈❡❧②✱ ❞✐r❡❝t❧② ❢r♦♠ t❤❡ ❈❉❙
s♣r❡❛❞s ❜② ✉s✐♥❣ ❛ ❞✐s❝r❡t❡✲t✐♠❡ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ ❞❡✜♥❡❞ ❜❡❧♦✇✽ ✳
❖♥ ♦♥❡ ❤❛♥❞✱ ❡q✉❛t✐♦♥ ✭✻✮ ❞❡✜♥❡❞ ❛❜♦✈❡ ❞♦❡s ♥♦t ❤❛✈❡ ❛♥② ❧✐q✉✐❞✐t② ❛❞❥✉st♠❡♥t ❛♥❞
✐♥❝❧✉❞❡s ♦♥❧② ❛ ❞❡❢❛✉❧t ❝♦♠♣♦♥❡♥t✾ ✳ ❙✐♥❝❡ ✇❡ ♣♦st✉❧❛t❡ t❤❛t t❤❡ ❛s❦ q✉♦t❡ ✐s t❤❡ ✉♣♣❡r ❜♦✉♥❞
✈❛❧✉❡ ❢♦r t❤❡ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ ❈❉❙ s♣r❡❛❞ sT ✱ ✇❡ ✉s❡ t❤❡ s❛♠❡ q✉♦t❡ t♦ r❡tr✐❡✈❡ t❤❡ ✐♠♣❧✐❡❞
❞❡❢❛✉❧t ✐♥t❡♥s✐t② h✳ ❚❤❡ ✐❞❡❛ ❝❛♥ ❜❡ ✐❧❧✉str❛t❡❞ ❛s ❢♦❧❧♦✇s✿
sask
T
2K
2K
j=1
j=1
X
1X
∗(
P (j/2).Q(j/2, h)) = (1 − w) ∗
P (j/2)[Q(j − 1/2, h) − Q(j/2, h)]
2
✭✶✵✮
P (j/2) ❛♥❞ Q(j/2, h) r❡♣r❡s❡♥t t❤❡ r✐s❦ ❢r❡❡ ❞✐s❝♦✉♥t ❢❛❝t♦r ❛♥❞ t❤❡ r✐s❦✲♥❡✉tr❛❧ s✉r✈✐✈❛❧
♣r♦❜❛❜✐❧✐t② r❡s♣❡❝t✐✈❡❧②✱ K ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❈❉❙ ♠❛t✉r✐t② ❛♥❞ w t♦ t❤❡ r❡❝♦✈❡r② r❛t❡✳ ❇♦t❤
✼
■♥ t❤✐s st✉❞②✱ ✇❡ ✉s❡ t❤❡ t❡r♠s ❤❛③❛r❞ r❛t❡ ❛♥❞ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ✐♥t❡r❝❤❛♥❣❡❛❜❧②✳
❇❡r♥❞t ❛♥❞ ❖❜r❡❥❛ ✭✷✵✶✵✮ ✉s❡ s✐♠✐❧❛r t②♣❡ ♦❢ ❞✐s❝r❡t✐③❛t✐♦♥ ❢♦r t❤❡ ❝♦r♣♦r❛t❡ ❈❉❙s✳
✾
❲❡ ♦♣t ❢♦r ❛ s✐♠♣❧❡ ❝r❡❞✐t r✐s❦ ♠♦❞❡❧ ✐♥ ♦r❞❡r t♦ s✐♠♣❧✐❢② t❤❡ ✐s♦❧❛t✐♦♥ ♦❢ ❝r❡❞✐t r✐s❦ ❛♥❞ t❤❡r❡❢♦r❡ ❛❧❧♦✇
t❤❡ ❢♦❝✉s ♦♥ ❧✐q✉✐❞✐t② r✐s❦ ✇❤✐❝❤ ✇❡ ❜❡❧✐❡✈❡ ✐s t❤❡ ♠❛✐♥ s♦✉r❝❡ ♦❢ t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❜♦t❤ ✐♥str✉♠❡♥ts✳
❆ss✉♠✐♥❣ ❛ ♠♦r❡ ❝♦♠♣❧❡① ❝r❡❞✐t r✐s❦ ♠♦❞❡❧ t♦ ✐s♦❧❛t❡ ❧✐q✉✐❞✐t② r✐s❦ ♠❛② ♥♦t ❜❡ ❤❡❧♣❢✉❧✳ ❈r❡❞✐t r✐s❦ ✐♠♣❛❝ts ❜♦t❤
❜♦♥❞s ❛♥❞ ❈❉❙s ✇✐t❤ ❛ ❝♦♠♠♦♥ ✉♥❞❡r❧②✐♥❣ s✐♠✐❧❛r❧② ❛♥❞ t❤❡r❡❢♦r❡ ✇✐❧❧ ♥♦t ❝❤❛♥❣❡ t❤❡ ♦✈❡r❛❧❧ ✐♥t❡r♣r❡t❛t✐♦♥
♦❢ ♦✉r r❡s✉❧ts✳
✽
✶✵
❛♥❞ Q(j/2, h) ❛r❡ ❞✐✈✐❞❡❞ ❜② t✇♦ ✐♥ ♦r❞❡r t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ s❡♠✐✲❛♥♥✉❛❧ ♣❛②♠❡♥t✳ ❲❡
❛ss✉♠❡ ❛ ❝♦♥st❛♥t r✐s❦ ♥❡✉tr❛❧ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② h ✇❤✐❝❤ ❧❡❛❞s t♦ ❛ s✉r✈✐✈❛❧ ♣r♦❜❛❜✐❧✐t② ❡q✉❛❧
t♦✿
P (j/2)
✭✶✶✮
L = (1 − w) ✐s t❤❡ r✐s❦ ♥❡✉tr❛❧ ❧♦ss r❛t❡✶✵ ✐♥ t❤❡ ❡✈❡♥t ♦❢ ❞❡❢❛✉❧t ❛♥❞ ✐s ❡q✉❛❧ t♦ ✼✺✪ ✭P❛♥ ❛♥❞
❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮✮✳ ❚❤❡ ❧❡❢t ❤❛♥❞ s✐❞❡ ♦❢ ❡q✉❛t✐♦♥ ✭✶✵✮ r❡♣r❡s❡♥ts t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ♣r♦t❡❝t✐♦♥
❧❡❣ ❛♥❞ t❤❡ r✐❣❤t ❤❛♥❞ s✐❞❡ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❧❡❣ ❛t t❤❡ ✐♥✐t✐❛t✐♦♥ ♦❢ t❤❡ ❝♦♥tr❛❝t✳
h/2 − 1)
❇② r❡❛rr❛♥❣✐♥❣ ❡q✉❛t✐♦♥ ✭✶✵✮✱ ✇❡ ❝❛♥ ✐♥❢❡r t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ❢r♦♠ sask
T /2 = L(e
✇❤✐❝❤ ❧❡❛❞s t♦✿
Q(j/2, h) = e−h∗j/2
h = 2 ∗ log(1 +
sask
T
)
2 ∗ (1 − w)
✭✶✷✮
❊q✉❛t✐♦♥ ✭✶✷✮ r❡♣r❡s❡♥ts t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ✐♠♣❧✐❡❞ ❢r♦♠ t❤❡ ❈❉❙ ❛s❦ q✉♦t❡ ✇❤❡r❡
= sT ✳
❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ❡q✉❛t✐♦♥ ✭✼✮ ❝♦♥t❛✐♥s ❛ ♣❡♥❛❧t② ❢♦r ✐❧❧✐q✉✐❞✐t② ❛♥❞ ❛ ❞❡❢❛✉❧t ❛❞❥✉st♠❡♥t✳
❙✐♥❝❡ ✇❡ ❛ss✉♠❡❞ t❤❛t t❤❡ ❈❉❙ s♣r❡❛❞s ✐♥ t❤❡ ♠❛r❦❡t s∗T ❛r❡ ✐❧❧✐q✉✐❞ ✭♦r ♥♦t ♣❡r❢❡❝t❧② ❧✐q✉✐❞✮
❛♥❞ t❤❡r❡❢♦r❡ ❧❡ss t❤❛♥ t❤❡ ❛s❦ q✉♦t❡s✱ ✇❡ ✉s❡ t❤❡ ❈❉❙ ♠✐❞ q✉♦t❡s✶✶ t♦ r❡tr✐❡✈❡ t❤❡ ✐♠♣❧✐❡❞
❞❡❢❛✉❧t ✐♥t❡♥s✐t② ❛♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✭h ❛♥❞ y r❡s♣❡❝t✐✈❡❧②✮✳ ❚❤✉s✱ ✇❡ ❞✐s❝r❡t✐③❡ ❡q✉❛t✐♦♥ ✭✼✮
❛♥❞ r❡tr✐❡✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛✿
sask
T
s∗T ∗(
2K
2K
j=1
j=1
X
1X
P (j/2).Q(j/2, h)) = (1−w)∗
P (j/2)[Q(j−1/2, h)−Q(j/2, h)]∗LCDS (j/2, y CDS )
2
✇❤❡r❡
✭✶✸✮
✭✶✹✮
❲❡ ❝❛❧✐❜r❛t❡ ❡q✉❛t✐♦♥ ✭✶✸✮ t♦ t❤❡ ❈❉❙ ♠✐❞ q✉♦t❡s ✇❤✐❝❤ ❛r❡ ❛❧r❡❛❞② ❛❞❥✉st❡❞ ❢♦r ✐❧❧✐q✲
✉✐❞✐t② ✭s✐♥❝❡ t❤❡② ❛r❡ ❧♦✇❡r t❤❛♥ t❤❡ ❈❉❙ ❛s❦ q✉♦t❡s✮✱ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ❞✐s❝♦✉♥t ❢❛❝t♦r
LCDS (j/2, y CDS ) ✇✐❧❧ ✈❛♥✐s❤ ❛♥❞ t❤✉s ❡q✉❛t✐♦♥ ✭✶✸✮ ❝♦✉❧❞ ❜❡ r❡✇r✐tt❡♥ ❛s✿
LCDS (j/2, y CDS ) = e−y
✶✵
CDS ∗j/2
❲❡ r❡❞♦ t❤❡ s❛♠❡ ❛♥❛❧②s✐s ❜② tr②✐♥❣ ❞✐✛❡r❡♥t ✈❛❧✉❡s ❢♦r t❤❡ ❧♦ss r❛t❡ ✭✺✵✪✱ ✻✵✪✱ ✾✵✪✮ ❛♥❞ ❛❧t❤♦✉❣❤ ✐t
✐♥✢✉❡♥❝❡s t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ t❤❡ ❤❛③❛r❞ r❛t❡ ❛♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✐t ❞♦❡s♥t ❝❤❛♥❣❡ t❤❡ r❡s✉❧ts ❞❡s❝r✐❜❡❞
❛❜♦✈❡✳
✶✶
■♥ t❤✐s st✉❞②✱ ✇❡ ❛ss✉♠❡ t❤❛t t❤❡ ❈❉❙ ♠✐❞ q✉♦t❡ ✐s ❛ ❢❛✐r r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣r✐❝❡ ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝t✳
✶✶
smid
∗(
T
2K
2K
j=1
j=1
X
1X
P (j/2).Q∗ (j/2, h∗ )) = (1 − w) ∗
P (j/2)[Q∗ (j − 1/2, h∗ ) − Q∗ (j/2, h∗ )] ✭✶✺✮
2
✇❤❡r❡
Q∗ (j/2, h∗ ) = e−h
✭✶✻✮
∗ ∗j/2
h∗ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❤❛③❛r❞ r❛t❡ ❛❞❥✉st❡❞ ❢♦r ✐❧❧✐q✉✐❞✐t② ❛s ✐t ✐s r❡tr✐❡✈❡❞ ❢r♦♠ t❤❡ ❈❉❙
♠✐❞ q✉♦t❡s✳ ■♥ ♦t❤❡r t❡r♠s✱ h∗ = h − y CDS ✳
❇② ❞✐s❝r❡t✐③✐♥❣ ❡q✉❛t✐♦♥ ✭✶✺✮✱ ✇❡ ♦❜t❛✐♥✿
h∗ = 2 ∗ log(1 +
smid
T
)
2 ∗ (1 − w)
✭✶✼✮
❊q✉❛t✐♦♥ ✭✶✼✮ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ❛❞❥✉st❡❞ ❢♦r ✐❧❧✐q✉✐❞✐t② ✐♠♣❧✐❡❞ ❢r♦♠ t❤❡
❈❉❙ ♠✐❞ q✉♦t❡ smid
T ✳ ❚❤✉s ❜② t❛❦✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❡q✉❛t✐♦♥ ✭✶✼✮ ❛♥❞ ✭✶✷✮✱ ✇❡ ❝♦✉❧❞
r♦✉❣❤❧② ✐s♦❧❛t❡ t❤❡ ♣✉r❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② h ❛♥❞ ❢♦❝✉s ♦♥ ❧✐q✉✐❞✐t② r✐s❦ y CDS ✳ ❚❤❡ ♥❡✇ ✈❛r✐❛❜❧❡
zCDS = h − h∗ ✇✐❧❧ t❤✉s s❡r✈❡ ❛s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦✶✷ ✳
❲❡ r❡❞♦ t❤❡ s❛♠❡ ❛♥❛❧②s✐s ❛❝r♦ss t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s ✭✐✳❡ ❢♦r t❤❡
✶②✱ ✸②✱ ✺②✱ ✼② ❛♥❞ ✶✵② ♠❛t✉r✐t②✮ ❛♥❞ ✇❡ ♣❧♦t t❤❡ t✐♠❡ s❡r✐❡s ♦❢ t❤❡ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢
t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ t❡r♠ str✉❝t✉r❡ ♦❢ ❇r❛③✐❧ ✭❋✐❣✉r❡ ✶✮✱ P❤✐❧✐♣♣✐♥❡s ✭❋✐❣✉r❡ ✷✮ ❛♥❞ ❚✉r❦❡②
✭❋✐❣✉r❡ ✸✮✳
❖✈❡r❛❧❧✱ t❤❡ ✜❣✉r❡s s❤♦✇ t❤❛t ❢♦r t❤❡ ♣❡r✐♦❞ ♣r❡❝❡❞✐♥❣ t❤❡ ❝r✐s✐s t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❈❉❙
❧✐q✉✐❞✐t② r✐s❦ ❤❛s ❛ ✢❛t ❜❡❤❛✈✐♦r ❡s♣❡❝✐❛❧❧② ❢♦r ❚✉r❦❡② ❛♥❞ P❤✐❧✐♣♣✐♥❡s✱ ❛❧t❤♦✉❣❤ ✇❡ ♦❜s❡r✈❡
t❤❛t ❧✐q✉✐❞✐t② r✐s❦ ✐s s❧✐❣❤t❧② ❤✐❣❤❡r ❢♦r t❤❡ s❤♦rt ❛♥❞ t❤❡ ❧♦♥❣ ❡♥❞ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡✳ ❚❤❡
❝❛s❡ ♦❢ ❇r❛③✐❧ ✐s ❞✐✛❡r❡♥t ❛s ✇❡ s❡❡ t❤❛t t❤❡ ✜rst ♣❛rt ♦❢ t❤❡ s❛♠♣❧❡ ✐s ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❢❡✇
s♣✐❦❡s ❜✉t t❤❡ t❡r♠ str✉❝t✉r❡ ✢❛tt❡♥s s✐♠✐❧❛r❧② t♦ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✳ ❉✉r✐♥❣ t❤❡ ❝r✐s✐s
♣❡r✐♦❞ ❛♥❞ ❢♦r ❛❧❧ t❤❡ ❝♦✉♥tr✐❡s✱ ✇❡ ♦❜s❡r✈❡ t❤❛t t❤❡ s❤❛♣❡ ♦❢ t❤❡ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡
❧✐q✉✐❞✐t② r✐s❦ t❡r♠ str✉❝t✉r❡ ✐s ✐♥✈❡rt❡❞ ✇✐t❤ t❤❡ s❤♦rt ❡♥❞ ❤❛✈✐♥❣ ❤✐❣❤❡r ✈❛❧✉❡s t❤❛♥ t❤❡ ❧♦♥❣
❡♥❞ ♦❢ t❤❡ ❝✉r✈❡✳ ❚❤✐s r❡s✉❧t ♣♦✐♥ts t♦ t❤❡ ❢❛❝t t❤❛t ❧✐q✉✐❞✐t② r✐s❦ ✐s ♣r❡ss✉r✐③✐♥❣ ♠♦r❡ ❛t t❤❡
s❤♦rt ❡♥❞ ♦❢ t❤❡ ❈❉❙ ❝✉r✈❡✳ ■♥ t❤❡✐r st✉❞② P❛♥ ❛♥❞ ❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮ ✜♥❞ t❤❛t t❤❡✐r ❧♦❣✲♥♦r♠❛❧
♦♥❡ ❢❛❝t♦r ♠♦❞❡❧ ❝❛♣t✉r❡s q✉✐t❡ ✇❡❧❧ t❤❡ ❜❡❤❛✈✐♦r ♦❢ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ t❡r♠ str✉❝t✉r❡ ❜✉t
♠✐s♣r✐❝❡s t❤❡ ✶ ②❡❛r ❈❉❙ ❝♦♥tr❛❝t✳ ❚❤❡ ❛✉t❤♦rs ♣r♦✈✐❞❡ ❛s ❛ ♣♦ss✐❜❧❡ ❡①♣❧❛♥❛t✐♦♥ t❤❡ ❧✐q✉✐❞✐t②
❛♥❞✴♦r t❤❡ ❡✛❡❝ts ♦❢ s✉♣♣❧② ❛♥❞ ❞❡♠❛♥❞ ♣r❡ss✉r❡s✳
✶✷
❚❤❡
s❛♠❡
✈❛r✐❛❜❧❡
zCDS
✇✐❧❧
❜❡
✉s❡❞
✐♥
s❡❝t✐♦♥
LCDS (j/2, y CDS )✳
✶✷
✼
t♦
❡st✐♠❛t❡
t❤❡
❧✐q✉✐❞✐t②
r✐s❦
❞✐s❝♦✉♥t
❢❛❝t♦r
■♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s✉❜s❡❝t✐♦♥✱ ✇❡ ❡①tr❛❝t ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✐♥ ❛ s✐♠✐❧❛r ♠❛♥♥❡r t♦ t❤❡ ❈❉❙
♠❛r❦❡t✳ ❚❤❡ ❧✐q✉✐❞✐t② ♦❢ t❤❡ ✉♥❞❡r❧②✐♥❣ ❜♦♥❞ ♠❛r❦❡t ✐s ❛❧s♦ ✐♠♣♦rt❛♥t t♦ ❝♦♥s✐❞❡r ❜❡❝❛✉s❡
❈❉❙ tr❛❞❡rs ❤❡❞❣❡ t❤❡✐r ♣♦s✐t✐♦♥s ✇✐t❤ ❝❛s❤ ♠❛r❦❡t ✐♥str✉♠❡♥ts ❛♥❞ t❤❡ ❤✐❣❤❡r t❤❡ ❧✐q✉✐❞✐t②
r✐s❦ ✐♥ t❤❡ ❜♦♥❞ ♠❛r❦❡t t❤❡ ❤✐❣❤❡r t❤❡ ✐♠♣❛❝t ♦♥ ❈❉❙ s♣r❡❛❞s✳
✺✳✷
❇♦♥❞ ❉✐s❝r❡t✐③❛t✐♦♥✿
❲❡ ❞✐s❝r❡t✐③❡ t❤❡ ❜♦♥❞ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ ✐♥ ❛ s✐♠✐❧❛r ❢❛s❤✐♦♥ t♦ t❤❡ ❈❉❙ ♠❛r❦❡t ✐♥ ♦r❞❡r t♦
❡①tr❛❝t ❛♥ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✳
ask ✐s ❞❡✜♥❡❞ ❛s✿
❖♥ ♦♥❡ ❤❛♥❞✱ t❤❡ ♣❡r❢❡❝t❧② ❧✐q✉✐❞ ❜♦♥❞ ♣r✐❝❡ VBond
ask
VBond
=c
n
X
j=1
F
1
+
ask
j
(1 + x )
(1 + xask )n
✭✶✽✮
✇❤❡r❡ c ✐s t❤❡ ❝♦✉♣♦♥ r❛t❡✱ F t❤❡ ❢❛❝❡ ✈❛❧✉❡ ❛♥❞ xask t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♦❢ t❤❡ ♣❡r❢❡❝t❧②
❧✐q✉✐❞ ❜♦♥❞✳
mid tr❛❞❡❞ ✐♥ t❤❡ ♠❛r❦❡t ✐s ❞❡✜♥❡❞ ❛s✿
❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ t❤❡ ✐❧❧✐q✉✐❞ ❜♦♥❞ ♣r✐❝❡ VBond
mid
VBond
=c
n
X
j=1
F
1
+
mid
j
(1 + x )
(1 + xmid )n
✭✶✾✮
✇❤❡r❡ xmid ✐s t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♦❢ t❤❡ ✐❧❧✐q✉✐❞ ❜♦♥❞ ❛♥❞ ✐s ❡q✉❛❧ t♦ xmid = xask + y bond
✇❤❡r❡ y bond ✐s ❧✐q✉✐❞✐t② r✐s❦✳
ask > V mid ❛♥❞ xask < xmid t❤✉s ♦✉r ♥❡✇ ✈❛r✐❛❜❧❡ z
mid − xask r❡♣r❡s❡♥ts
❙✐♥❝❡ VBond
bond= x
Bond
♦✉r ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✳
✺✳✸
❚❤❡ ❚❡r♠ ❙tr✉❝t✉r❡ ♦❢ ❇♦♥❞ ❛♥❞ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦✿ ❆ ❈♦♠♣❛r❛t✐✈❡
❆♥❛❧②s✐s
❲❡ ❞♦ ❛ ❝♦♠♣❛r❛t✐✈❡ ❛♥❛❧②s✐s ❜❡t✇❡❡♥ t❤❡ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t②
r✐s❦ ❛t ❝♦♥st❛♥t ♠❛t✉r✐t②✳ ❚♦ t❤✐s ❡♥❞✱ ✇❡ ♥❡❡❞ t♦ ♠❛t❝❤ ❜♦♥❞ ❛♥❞ ❈❉❙ ♠❛t✉r✐t✐❡s ✭✐✳❡✳ ✶✱
✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs✮ ✐♥ ♦r❞❡r t♦ ✐s♦❧❛t❡ t❤❡ ♠❛t✉r✐t② ❡✛❡❝t✳ ❚❤❡r❡❢♦r❡ ❢♦r t❤❡ ✶ ②❡❛r ❈❉❙
✇❡ s❤♦✉❧❞ ❤❛✈❡ ❜♦♥❞s t❤❛t ♠❛t✉r❡ ❜❡t✇❡❡♥ ✷✵✵✻ ❛♥❞ ✷✵✶✶✶✸ ✱ ❢♦r t❤❡ ✸ ②❡❛r ❈❉❙ ✇❡ ♥❡❡❞
✶✸
❚❤✐s ✐s ❞✉❡ t♦ t❤❡ ❢❛❝t t❤❛t ♦✉r s❛♠♣❧❡ ♣❡r✐♦❞ s♣❛♥s ❢r♦♠ ◆♦✈❡♠❜❡r ✷✵✵✺ t♦ ❙❡♣t❡♠❜❡r ✷✵✶✵✳
✶✸
❜♦♥❞s t❤❛t ♠❛t✉r❡ ❜❡t✇❡❡♥ ✷✵✵✽ ❛♥❞ ✷✵✶✸✱ ❢♦r t❤❡ ✺ ②❡❛r ❈❉❙ ✇❡ r❡q✉✐r❡ ❜♦♥❞s ♠❛t✉r✐♥❣
❜❡t✇❡❡♥ ✷✵✶✵ ❛♥❞ ✷✵✶✺✱ ❢♦r t❤❡ ✼ ②❡❛r ❈❉❙ ✇❡ s❤♦✉❧❞ ✉s❡ ❜♦♥❞s ♠❛t✉r✐♥❣ ❜❡t✇❡❡♥ ✷✵✶✷ ❛♥❞
✷✵✶✼ ❛♥❞ ✜♥❛❧❧② ❢♦r t❤❡ ✶✵ ②❡❛r ❈❉❙ ✇❡ s❤♦✉❧❞ ❤❛✈❡ ❜♦♥❞s ♠❛t✉r✐♥❣ ❜❡t✇❡❡♥ ✷✵✶✵ ❛♥❞ ✷✵✷✵✳
❆❧t❤♦✉❣❤ t❤❡ ❝♦✉♥tr✐❡s ✇❡ ♣✐❝❦❡❞ ❤❛✈❡ ❛ ❧❛r❣❡ ❛♠♦✉♥t ♦❢ ❜♦♥❞s ✐ss✉❡❞ ❛t ❞✐✛❡r❡♥t ❞❛t❡s✶✹ ✱ ✐t
✐s ♥♦t ❡♥♦✉❣❤ t♦ ♠❛t❝❤ ❛❧❧ ❈❉❙ ♠❛t✉r✐t✐❡s✳ ❍♦✇❡✈❡r ❢♦r ❡❛❝❤ ❈❉❙ ♠❛t✉r✐t② ✇❡ ♣✐❝❦ ❜♦♥❞
t❤❛t ❢❛❧❧ ✐♥t♦ t❤❡ ♠❛t✉r✐t② ✐♥t❡r✈❛❧s ♠❡♥t✐♦♥❡❞ ❛❜♦✈❡✳ ❚❤❡r❡❢♦r❡✱ ✐♥ ♦r❞❡r t♦ ♣r♦①② ❢♦r t❤❡ ✶
②❡❛r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✇❡ ✉s❡ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ♠✐❞ ❛♥❞ ❛s❦ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♦❢
t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❡ ❤❛✈❡ ❢♦r ❡❛❝❤ ❝♦✉♥tr② ✭✐✳❡✳ ✵✷✴✷✵✶✸ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✽✴✷✵✶✶
❢♦r ❇r❛③✐❧ ❛♥❞ ✵✻✴✷✵✶✶ ❢♦r ❚✉r❦❡②✮✳ ▲✐❦❡✇✐s❡✱ ✇❡ ♣r♦①② ❧✐q✉✐❞✐t② r✐s❦ ♦❢ t❤❡ ✸ ②❡❛r ❜♦♥❞ ❜②
t❛❦✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ♠✐❞ ❛♥❞ ❛s❦ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♦❢ ❜♦♥❞s t❤❛t ❡①♣✐r❡ r✐❣❤t
❛❢t❡r t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞s ✭✐✳❡✳ ✵✶✴✷✵✶✹ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✶✷ ❢♦r ❇r❛③✐❧✱ ✵✶✴✷✵✶✸
❢♦r ❚✉r❦❡②✮✳ ❋♦r t❤❡ ✺ ②❡❛r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✱ ✇❡ ❝❤♦♦s❡ ❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❞♦
♥♦t ❡①❝❡❡❞ ✷✵✶✺ ✭✐✳❡✳ ✵✸✴✷✵✶✺ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✸✴✷✵✶✺ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✸✴✷✵✶✺ ❢♦r ❚✉r❦❡②✮✳ ❋♦r
t❤❡ ✼ ②❡❛r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✱ ✇❡ ♣✐❝❦ ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❛r❡ ❛r♦✉♥❞ ✷✵✶✼
✭✐✳❡✳ ✵✶✴✷✵✶✼ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✶✽ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✼✴✷✵✶✼ ❢♦r ❚✉r❦❡②✮ ❛♥❞ ✜♥❛❧❧② ✇❡ ❞♦ t❤❡
s❛♠❡ ❡①❡r❝✐s❡ ❢♦r t❤❡ ✶✵ ②❡❛r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✇❤❡r❡ ✇❡ ❝♦❧❧❡❝t ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t✐❡s
t❤❛t ❛r❡ ❛s ❝❧♦s❡ ❛s ♣♦ss✐❜❧❡ t♦ ✷✵✷✵ ✭✐✳❡✳ ✶✵✴✷✵✷✹ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✷✵ ❇r❛③✐❧ ❛♥❞ ✵✷✴✷✵✷✺
❚✉r❦❡②✮✶✺ ✳
❆s ❛ ❢✉rt❤❡r st❡♣✱ ✇❡ ♣❧♦t t❤❡ r❛t✐♦ ♦❢ t❤❡ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t②
r✐s❦ t❡r♠ str✉❝t✉r❡s ✭✐✳❡✳ zzCDS
✮ ✐♥ ♦r❞❡r t♦ ❛♥❛❧②s❡ t❤❡✐r ❥♦✐♥t ❜❡❤❛✈✐♦r✳ ❚❤❡ r❡s✉❧ts ❛r❡ s❤♦✇♥
bond
✐♥ ❋✐❣✉r❡s ✹✱ ✺ ❛♥❞ ✻✳
❋♦r ❇r❛③✐❧✱ ❋✐❣✉r❡ ✹ s❤♦✇s t❤❛t ❛t t❤❡ s❤♦rt✲❡♥❞ ♦❢ t❤❡ ❝✉r✈❡ ✇❡ ❤❛✈❡ ❛ ❧♦✇ ❧✐q✉✐❞✐t② r✐s❦
r❛t✐♦ ✇❤✐❝❤ ✐♠♣❧✐❡s t❤❛t ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❤✐❣❤❡r t❤❛♥ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦✶✻ ✳ ❍♦✇❡✈❡r
❞✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✱ ✇❡ ♦❜s❡r✈❡ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ✇❤✐❝❤ ♣✉s❤❡s ✉♣ t❤❡
zCDS
zbond r❛t✐♦✱ t❤✐s r❡s✉❧t ✐♥❞✐❝❛t❡s t❤❛t ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐♥❝r❡❛s❡s ♠♦r❡ str♦♥❣❧② t❤❛♥ ❜♦♥❞
❧✐q✉✐❞✐t② r✐s❦✶✼ ✳ ❋✉rt❤❡r♠♦r❡✱ ❞✉r✐♥❣ t❤❡ ❝r✐s✐s t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ t❤❡ ✐♥❝r❡❛s❡ ✐♥ t❤❡ zzCDS
bond
r❛t✐♦ ✐s ❤✐❣❤❡r ❢♦r t❤❡ ❧♦♥❣ ❡♥❞ ♦❢ t❤❡ ❝✉r✈❡ t❤❛♥ ❢♦r t❤❡ s❤♦rt ❡♥❞ ✇❤✐❝❤ ✐♠♣❧✐❡s t❤❛t ❧♦♥❣❡r
♠❛t✉r✐t✐❡s ❛r❡ ♠♦r❡ s❡♥s✐t✐✈❡ t♦ t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ❝❤❛♥❣❡s✳ ❚❤✐s r❡s✉❧t ✐s ✐♥t✉✐t✐✈❡ ❛s t❤❡r❡
✶✹
❚❛❜❧❡ ✶ ♣r❡s❡♥ts ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ ♦✉r ❜♦♥❞ ❞❛t❛s❡t ✇✐t❤ ✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡ ❛✈❡r❛❣❡ ♠✐❞ ②✐❡❧❞✱ ♠❛t✉r✐t②
❞❛t❡s✱ ❝♦✉♣♦♥ ♣❛②♠❡♥t r❛t❡s ❛♥❞ ✐ss✉❡ ❞❛t❡s✳
✶✺
❋♦r s❛❦❡ ♦❢ ❝♦♠♣❛r✐s♦♥✱ ❚❛❜❧❡ ✷ ♣r❡s❡♥ts ❛ ❞❡s❝r✐♣t✐✈❡ st❛t✐st✐❝s ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙ ❜✐❞✲❛s❦ s♣r❡❛❞s ❛t
♠❛t❝❤❡❞ ♠❛t✉r✐t✐❡s✳
✶✻
■♥ t❤❡ ❧♦♥❣ ❡♥❞ ♦❢ t❤❡ ❝✉r✈❡ ✇❡ ♦❜s❡r✈❡ ❢❡✇ s♣✐❦❡s ✐♥ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✇❤✐❝❤ ♣✉s❤ t❤❡ r❛t✐♦
zCDS
t♦
zbond
❛ ❤✐❣❤ ❧❡✈❡❧✳
✶✼
❲❤❡♥ ✇❡ ♣❧♦t t❤❡ t✐♠❡ s❡r✐❡s ♦❢ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✇❡ s❡❡ t❤❛t ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✐♥❝r❡❛s❡s ❞✉r✐♥❣ ❝r✐s✐s
t✐♠❡✱ t❤✐s ✐s ✈❛❧✐❞ ❢♦r ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✳
✶✹
✐s ♠♦r❡ ✉♥❝❡rt❛✐♥t② ♦♥ ❧♦♥❣❡r ♠❛t✉r✐t✐❡s✳
❆s ❢❛r ❛s P❤✐❧✐♣♣✐♥❡s ✐s ❝♦♥❝❡r♥❡❞✱ ❋✐❣✉r❡ ✺ ❡①❤✐❜✐ts ❛ ❞✐✛❡r❡♥t ❜❡❤❛✈✐♦r✳ ❖♥ ♦♥❡ ❤❛♥❞✱
❜❡❢♦r❡ t❤❡ ❝r✐s✐s✱ ✇❡ s❡❡ t❤❛t ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❤✐❣❤❡r t❤❛♥ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❛❝r♦ss t❤❡
✇❤♦❧❡ t❡r♠ str✉❝t✉r❡✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ❞✉r✐♥❣ t❤❡ ❝r✐s✐s✱ t❤❡ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t②
✐♠♣❛❝ts t❤❡ ❧✐q✉✐❞✐t② r✐s❦ r❛t✐♦ zzCDS
✐♥ ❛ s✐♠✐❧❛r ♠❛♥♥❡r ❛❝r♦ss t❤❡ ✇❤♦❧❡ t❡r♠ str✉❝t✉r❡ ✇✐t❤
bond
❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐♥❝r❡❛s✐♥❣ ♠♦r❡ str♦♥❣❧② t❤❛♥ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✳
❋✐♥❛❧❧② ❢♦r ❚✉r❦❡② ✇❡ ♦❜s❡r✈❡ ✐♥ ❋✐❣✉r❡ ✻ t❤❛t t❤❡ s❤♦rt ❡♥❞ ♦❢ t❤❡ ❝✉r✈❡ ❤❛s ❛ st❛❜❧❡
❧✐q✉✐❞✐t② r✐s❦ r❛t✐♦ ✭♦❢ ❛❜♦✉t ✶✮✳ ❉✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✱ t❤❡ r❛t✐♦ st❛②s ❛t ❛r♦✉♥❞ ✶ ✇❤✐❝❤
✐♥❞✐❝❛t❡s t❤❛t ❜♦t❤ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐♥❝r❡❛s❡ ✇✐t❤ t❤❡ s❛♠❡ ❞❡❣r❡❡✶✽ ✳ ❋✉rt❤❡r♠♦r❡✱
r❛t✐♦ ✐♠♣❧②✐♥❣ t❤❛t ❈❉❙ ❧✐q✉✐❞✐t②
t❤❡ ❧♦♥❣ ❡♥❞ ♦❢ t❤❡ ❝✉r✈❡ s❤♦✇s ❛ ❤✐❣❤ ✈❛❧✉❡ ♦❢ t❤❡ zzCDS
bond
r✐s❦ ✐s ❤✐❣❤❡r t❤❛♥ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✳
■♥ s✉♠♠❛r②✱ t❤❡ r❡s✉❧ts s❤♦✇ t❤❛t zzCDS
r❛t✐♦ ✐s ❧❛r❣❡❧② ✐♥✢✉❡♥❝❡❞ ❜② ❧✐q✉✐❞✐t② ✐ss✉❡s
bond
r❡❧❡✈❛♥t t♦ ❡❛❝❤ ❝♦✉♥tr②✱ ❤♦✇❡✈❡r ✇❡ r❡♣♦rt t❤❛t ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡ ❞❡❢❛✉❧t ✐♥t❡♥s✐t② ❝❤❛♥❣❡s
❞r❛♠❛t✐❝❛❧❧② t❤❡ r❛t✐♦ ❛s ✇❡ s❡❡ ❛ s✉r❣❡ ✐♥ ❧✐q✉✐❞✐t② r✐s❦ ✐♥ ❜♦t❤ ♠❛r❦❡ts ✇✐t❤ ❛ str♦♥❣❡r
✐♥❝r❡❛s❡ ❢r♦♠ t❤❡ ❈❉❙ s✐❞❡✳ ❖✉r ✜♥❞✐♥❣s ✐♠♣❧② t❤❛t t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙
✐❧❧✐q✉✐❞✐t② ✈❛r✐❡s ♦✈❡r t✐♠❡ ❛♥❞ ✐s str♦♥❣❧② ❞❡♣❡♥❞❡♥t ♦♥ t❤❡ ❣❡♥❡r❛❧ ✜♥❛♥❝✐❛❧ ❛♥❞ ❡❝♦♥♦♠✐❝
s✐t✉❛t✐♦♥✳
■♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s❡❝t✐♦♥✱ ✇❡ ♠♦❞❡❧ t❤❡ ❞②♥❛♠✐❝s ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✉s✐♥❣ ❛
❢❛❝t♦r ♠♦❞❡❧✳ ❇❡❢♦r❡ ❞♦✐♥❣ s♦✱ ✐t ✐s ✐♠♣♦rt❛♥t t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♥✉♠❜❡r ♦❢ ❢❛❝t♦rs t❤❛t ✇❡ ♥❡❡❞
t♦ ✉s❡ ✐♥ ♦r❞❡r t♦ ❝❛♣t✉r❡ ♠♦st ♦❢ t❤❡ ❧✐q✉✐❞✐t② ❞②♥❛♠✐❝s✳
✻ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s✿
■♥ t❤✐s s❡❝t✐♦♥✱ ✇❡ ♣❡r❢♦r♠ ❛ P❈ ❛♥❛❧②s✐s ✐♥ ♦r❞❡r t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♥✉♠❜❡r ♦❢ ❢❛❝t♦rs ♥❡❡❞❡❞
✐♥ t❤❡ ❢❛❝t♦r ♠♦❞❡❧✳ ❋♦r ❜♦t❤ ❈❉❙s ❛♥❞ ❜♦♥❞s✱ ✇❡ ❛♣♣❧② t❤❡ P❈ ❛♥❛❧②s✐s t♦ t❤❡ ♠✐❞ s♣r❡❛❞s
✭❜❡✐♥❣ ❛♥ ❛✈❡r❛❣❡ ♦❢ t❤❡ ❛s❦ ❛♥❞ t❤❡ ❜✐❞ q✉♦t❡s✮✶✾ ✳ ❆s ❛ ❢✉rt❤❡r st❡♣✱ ✇❡ ❛❧s♦ ❞♦ ❛ r♦❜✉st♥❡ss
❝❤❡❝❦ ✇❤❡r❡ ✇❡ ❛♣♣❧② t❤❡ P❈❆ t♦ t❤❡ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ ❧✐q✉✐❞✐t② r✐s❦ ❢♦r ❜♦t❤ ❈❉❙
✭zCDS ✮ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts ✭zbond ✮ ❛♥❞ ✇❡ ♦❜t❛✐♥ s✐♠✐❧❛r r❡s✉❧ts✳ ❚♦ s❛✈❡ s♣❛❝❡✱ ✇❡ ♦♥❧② s❤♦✇
t❤❡ P❈❆ r❡s✉❧ts ♦❢ t❤❡ ♠✐❞ q✉♦t❡s✳
❚❛❜❧❡ ✸ ❛♥❞ ❚❛❜❧❡ ✹ s✉♠♠❛r✐③❡ ♦✉r ♠❛✐♥ ✜♥❞✐♥❣s ❢♦r ❈❉❙s ❛♥❞ ❜♦♥❞s r❡s♣❡❝t✐✈❡❧②✳ ❲❡
♦❜s❡r✈❡ t❤❛t t❤❡ ✜rst P❈ ❝❛♣t✉r❡s ❛ s✐❣♥✐✜❝❛♥t ♣♦rt✐♦♥ ♦❢ t❤❡ s♣r❡❛❞ ✈❛r✐❛♥❝❡ ❢♦r ❛❧❧ ❝♦✉♥tr✐❡s✳
▼♦r❡♦✈❡r✱ t❤❡ ✜rst P❈ ❡♠❡r❣❡s ❛s ❛ ❧❡✈❡❧ ❢❛❝t♦r✱ ❛s r❡✢❡❝t❡❞ ✐♥ t❤❡ ✭r♦✉❣❤❧②✮ ❝♦♥st❛♥t ❢❛❝t♦r
❧♦❛❞✐♥❣s ❛❝r♦ss ♠❛t✉r✐t✐❡s✳ ❚❤✐s r❡s✉❧t ✐s ❝♦♥s✐st❡♥t ❛❝r♦ss ❝♦✉♥tr✐❡s✱ ♠❛r❦❡ts ❛♥❞ t✐♠❡ ♣❡r✐♦❞s✳
✶✽
❲❤❡♥ ✇❡ ♣❧♦t t❤❡ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐♥❞✐✈✐❞✉❛❧❧② ✇❡ ♦❜s❡r✈❡ ❛ s❤❛r♣ ✐♥❝r❡❛s❡ ✐♥ ❧✐q✉✐❞✐t② r✐s❦
✐♥ ❜♦t❤ ♠❛r❦❡ts✳
✶✾
❲❡ ❛♣♣❧② t❤❡ P❈ ❛♥❛❧②s✐s t♦ ❜♦♥❞s t❤❛t ❤❛✈❡ s✐♠✐❧❛r ♠❛t✉r✐t✐❡s t♦ t❤❡ ❈❉❙s✳
✶✺
❙❡❝♦♥❞❧②✱ t❤❡ s❡❝♦♥❞ P❈ s❤♦✇s ❛ ❞✐✛❡r❡♥t ❜❡❤❛✈✐♦✉r ✐♥ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✳ ❖♥ ♦♥❡
❤❛♥❞✱ ❢♦r t❤❡ ❝❛s❡ ♦❢ ❈❉❙s✱ t❤❡ s❡❝♦♥❞ P❈ ✐s ✐♥✈❡rs❡❧② r❡❧❛t❡❞ t♦ t✐♠❡ t♦ ♠❛t✉rt✐t②✳ ❖♥ t❤❡
♦t❤❡r ❤❛♥❞✱ ❢♦r t❤❡ ❝❛s❡ ♦❢ ❜♦♥❞s✱ t❤❡ s❡❝♦♥❞ P❈ r❡✢❡❝ts t❤❡ t✐♠❡✲t♦✲♠❛t✉r✐t② ❡✛❡❝t✷✵ ✳
❖✈❡r❛❧❧✱ ✐t s❡❡♠s t❤❛t ✉s✐♥❣ ❛ ♦♥❡ ❢❛❝t♦r ♠♦❞❡❧ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ❜♦♥❞ ❛♥❞ t❤❡ ❈❉❙ ♠❛r❦❡t
✐s s✉✣❝✐❡♥t t♦ ❝❛♣t✉r❡ ♠♦st ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ✈❛r✐❛t✐♦♥s✳
✼ ❊①♣♦♥❡♥t✐❛❧ ❆✣♥❡ ❋r❛♠❡✇♦r❦✿ ▲✐q✉✐❞✐t② ❘✐s❦ ❋❛❝t♦rs
■♥ t❤✐s s❡❝t✐♦♥✱ ✇❡ ♠♦❞❡❧ t❤❡ ❞②♥❛♠✐❝s ♦❢ t❤❡ ❜♦♥❞ ❛♥❞ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✉s✐♥❣ ❛ ♦♥❡
❢❛❝t♦r ❛✣♥❡ ♠♦❞❡❧✳ ❚❤❡ ♦♥❡ ❢❛❝t♦r ♠♦❞❡❧ ✐s ❥✉st✐✜❡❞ ❜② ♦✉r P❈ ❛♥❛❧②s✐s t❤❛t s❤♦✇❡❞ t❤❛t ♦♥❡
❢❛❝t♦r ❝❛♥ ❡①♣❧❛✐♥ ❛ s✉❜st❛♥t✐❛❧ ♣♦rt✐♦♥ ♦❢ t❤❡ ❧✐q✉✐❞✐t② ✈❛r✐❛t✐♦♥✳ ❲❡ ❛❧s♦ ♣♦st✉❧❛t❡ t❤❛t t❤❡
✉♥♦❜s❡r✈❛❜❧❡ st❛t❡ ✈❛r✐❛❜❧❡✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ❧✐q✉✐❞✐t② ❞②♥❛♠✐❝s✱ ❢♦❧❧♦✇s ❛ ❈■❘ ♣r♦❝❡ss✳ ❚❤❡
r❡❛s♦♥ ✐s ❜❡❝❛✉s❡ ✐♥ ♦✉r ♠♦❞❡❧ ✇❡ ❤②♣♦t❤❡t✐③❡ t❤❛t ❧✐q✉✐❞✐t② r✐s❦ r❡❞✉❝❡s t❤❡ ♣r✐❝❡ ♦❢ t❤❡ ❛ss❡t
✇❤✐❝❤ ✐♠♣❧✐❡s t❤❛t t❤❡ ✐❧❧✐q✉✐❞✐t② ❛❞❥✉st♠❡♥t t❤❛t ❡♥t❡rs t❤❡ ❜♦♥❞ ♦r ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛
❤❛s t♦ ❜❡ ♣♦s✐t✐✈❡✳ ❋✉rt❤❡r♠♦r❡✱ s✐♥❝❡ ✐♥ ♦✉r st✉❞②✱ ✇❡ ❛r❡ ❛ss✉♠✐♥❣ t❤❛t ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦
❞✐s❝♦✉♥t ❢❛❝t♦r ✐s ❞✐✛❡r❡♥t ❢r♦♠ t❤❛t ♦❢ t❤❡ ❜♦♥❞✱ ✇❡ ❡st✐♠❛t❡ t✇♦ ❞✐✛❡r❡♥t st❛t❡ ✈❛r✐❛❜❧❡s ✭✐✳❡✳
♦♥❡ st❛t❡ ✈❛r✐❛❜❧❡ s♣❡❝✐✜❝ t♦ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❞②♥❛♠✐❝s y CDS (t) ❛♥❞ ❛♥♦t❤❡r s♣❡❝✐✜❝
t♦ t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ❞②♥❛♠✐❝s y bond (t)✮✳ ❊❛❝❤ st❛t❡ ✈❛r✐❛❜❧❡ ❢♦❧❧♦✇s ❛ ❈■❘ ♣r♦❝❡ss ❛s
❞❡✜♥❡❞ ❜❡❧♦✇✳
p
y CDS ∗ dW1 (t)
✭✷✵✮
p
y bond ∗ dW2 (t)
✭✷✶✮
dy CDS (t) = (α1 µ1 − (α1 + λ1 ) ∗ y CDS (t)) ∗ dt + σ1
dy bond (t) = (α2 µ2 − (α2 + λ2 ) ∗ y bond (t)) ∗ dt + σ2
✇❤❡r❡ y CDS (t) ✭y bond (t)✮ r❡♣r❡s❡♥ts t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ ♦❢ t❤❡ ❈❉❙ ✭❜♦♥❞✮ ❧✐q✉✐❞✐t② r✐s❦✳ αi
❝♦rr❡s♣♦♥❞s t♦ t❤❡ ♠❡❛♥ r❡✈❡rs✐♦♥ s♣❡❡❞✱ µi t❤❡ ♠❡❛♥ r❡✈❡rs✐♦♥ ❧❡✈❡❧✱ σi t❤❡ ✈♦❧❛t✐❧✐t② ❛♥❞ λi
t❤❡ r✐s❦ ♣r❡♠✐✉♠ ✇✐t❤ i = 1, 2✳ dW1 (t) ∗ dW2 (t) = 0.
❋♦❧❧♦✇✐♥❣ ▲♦♥❣st❛✛✱ ▼✐t❤❛❧ ❛♥❞ ◆❡✐s ✭✷✵✵✺✮✱ ✇❡ ❞❡r✐✈❡ ❛ ❝❧♦s❡❞ ❢♦r♠ s♦❧✉t✐♦♥ ❢♦r t❤❡
❡①♣❡❝t❡❞ ✈❛❧✉❡ ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ❞✐s❝♦✉♥t ❢❛❝t♦r LCDS
t,s ✳ ❲❡ ❤❛✈❡✿
✷✵
❚❤❡ t✐♠❡ t♦ ♠❛t✉r✐t② ❡✛❡❝t ❞♦❡s ♥♦t s❤♦✇ ✐♥ ❚✉r❦❡② ❞✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✳
✶✻
LCDS
t,s
= E[exp(−
ˆ
s
✭✷✷✮
y CDS (u)du)]
t
✇❤❡r❡ s r❡♣r❡s❡♥ts t❤❡ ♠❛t✉r✐t② ❞❛t❡✳ ❲❡ s♦❧✈❡ ❢♦r LCDS
✉s✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ ❡①♣r❡ss✐♦♥✿
t,s
✭✷✸✮
LCDS
= A(t, s) ∗ exp(−y CDS (t) ∗ B(t, s))
t,s
✇❤❡r❡
A(t, s) = [
2 ∗ ξ1 ∗ exp(0.5 ∗ (α1 + ξ1 + λ1 ) ∗ (s − t))
]
2 ∗ ξ1 + (α1 + ξ1 + λ1 )(exp(ξ1 (s − t)) − 1)
2∗α1 ∗µ1
2
σ1
✭✷✹✮
✇✐t❤ s ❃ t ❛♥❞
B(t, s) = [
2 ∗ (exp(ξ1 (s − t)) − 1)
]
2 ∗ ξ1 + (α1 + ξ1 + λ1 )(exp(ξ1 (s − t)) − 1)
✭✷✺✮
✇✐t❤
q
ξ1 = (α1 + λ1 )2 + 2 ∗ σ12
✭✷✻✮
❙✐♠✐❧❛r❧②✱ ✇❡ s♦❧✈❡ ❢♦r t❤❡ ❡①♣❡❝t❡❞ ✈❛❧✉❡ ♦❢ t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② ❞✐s❝♦✉♥t ❢❛❝t♦r Lbond
❜②
t,s
bond
CDS
✉s✐♥❣ y (u) ✐♥st❡❛❞ ♦❢ y
(u)✳ ■♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s❡❝t✐♦♥✱ ✇❡ ❡st✐♠❛t❡ t❤❡ ❛✣♥❡ ♠♦❞❡❧ ✉s✐♥❣
t❤❡ ❑❛❧♠❛♥ ✜❧t❡r t❡❝❤♥✐q✉❡ ❞❡s❝r✐❜❡❞ ❜❡❧♦✇✳
✽ ❑❛❧♠❛♥ ❋✐❧t❡r ❊st✐♠❛t✐♦♥✿
■♥ ♦r❞❡r t♦ ❡st✐♠❛t❡ t❤❡ ♠♦❞❡❧ ❞❡s❝r✐❜❡❞ ❛❜♦✈❡ ❛♥❞ ❛tt❡♠♣t t♦ ✐❞❡♥t✐❢② t❤❡ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠ ♦r t❤❡ ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦ λi s♣❡❝✐✜❝ t♦ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✱ ✇❡ ✉s❡ ❛ st❛t❡
s♣❛❝❡ ❢♦r♠ t❤❛t ❛❧❧♦✇s t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ♠❡❛s✉r❡♠❡♥t ❡rr♦rs ✐♥ ❛❧❧ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛t✉r✐t✐❡s✳
✶✼
❚❤❡ ❑❛❧♠❛♥ ✜❧t❡r ❡st✐♠❛t✐♦♥ ❤❛s t❤❡ ❛❞✈❛♥t❛❣❡ ♦❢ s✐♠♣❧✐❢②✐♥❣ t❤❡ ❧✐❦❡❧✐❤♦♦❞ ❢✉♥❝t✐♦♥ ❛♥❞ t❤✉s
♣r♦✈✐❞❡s ❛ ❝❧❡❛r❡r ✐♥s✐❣❤t ♦♥ t❤❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ♦❢ t❤❡ ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦✳
✽✳✶
❙t❛t❡ ❙♣❛❝❡ ❘❡♣r❡s❡♥t❛t✐♦♥
❚❤❡ ♠♦❞❡❧ ❡①♣r❡ss❡❞ ✐♥ ❛ st❛t❡ s♣❛❝❡ ❢♦r♠ ✐♥✈♦❧✈❡s t❤❡ s♣❡❝✐✜❝❛t✐♦♥ ♦❢ t❤❡ ♠❡❛s✉r❡♠❡♥t
s②st❡♠ ❛♥❞ t❤❡ tr❛♥s✐t✐♦♥ s②st❡♠✳ ❚❤❡ ♠❡❛s✉r❡♠❡♥t ❡q✉❛t✐♦♥ r❡♣r❡s❡♥ts t❤❡ ❛✣♥❡ r❡❧❛t✐♦♥s❤✐♣
❜❡t✇❡❡♥ t❤❡ ♦❜s❡r✈❛t✐♦♥s ❛♥❞ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ y CDS (t)✳ ❚❤❡ tr❛♥s✐t✐♦♥ ❡q✉❛t✐♦♥ ❝♦rr❡s♣♦♥❞s
t♦ t❤❡ ❞②♥❛♠✐❝s ♦❢ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ y CDS (t) ❞❡✜♥❡❞ ❛❜♦✈❡✳ ❇② ❝♦♠❜✐♥✐♥❣ ❜♦t❤ ♦❜s❡r✈❛t✐♦♥s
❛♥❞ st❛t❡ ✈❛r✐❛❜❧❡ ✐♥ ❛ st❛t❡ s♣❛❝❡ ❢♦r♠ ✇❡ ❝❛♥ ❡st✐♠❛t❡ t❤❡ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ ♠♦❞❡❧ ❛♥❞
❛tt❡♠♣t t♦ ✐❞❡♥t✐❢② t❤❡ ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦✳ ❚❤❡ ❞❛t❛ ✉s❡❞ ✐♥ t❤❡ ♠❡❛s✉r❡♠❡♥t ❡q✉❛t✐♦♥ ✐s
t❤❡ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ zCDS (t, si ) ❞❡✜♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s s❡❝t✐♦♥✳
❆❧t❤♦✉❣❤ zCDS (t, si ) ✐s ❥✉st ❛ ♣r♦①② ❢♦r ❧✐q✉✐❞✐t② r✐s❦✱ ✐t ✐s st✐❧❧ ❛ ♠❡❛s✉r❡ t❤❛t ✐s ❢r❡❡ ♦❢ ❝r❡❞✐t
r✐s❦ ✇❤✐❝❤ ♠❛② ❤❡❧♣ ✉s ✐❞❡♥t✐❢② ✇❤❡t❤❡r t❤❡r❡ ✐s ❛♥② ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ λ1 ♣r✐❝❡❞ ✐♥ t❤❡
❈❉❙ ♠❛r❦❡t✳ ❚❤❡ st❛t❡ s♣❛❝❡ ❢♦r♠ ✐s ❞❡✜♥❡❞ ❛s ❢♦❧❧♦✇s✿
y CDS (t) = a + Φ ∗ y CDS (t − 1) + vt
zCDS (t, si ) = −
lnA(t, si ) B(t, si )
+
∗ y CDS (t) + εt
si − t
si − t
✭✷✼✮
✭✷✽✮
✇❤❡r❡ εt = (ε1 , ε3 , ε5 , ε7 , ε10 )✳ εi r❡♣r❡s❡♥ts t❤❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦r t❡r♠ t❤❛t ❢♦❧❧♦✇s ❛
♥♦r♠❛❧ ❞✐str✐❜✉t✐♦♥ ✭✐✳❡✳ εt ∼ N (0, U )✮ ❛♥❞ ✐s ✐♥tr♦❞✉❝❡❞ t♦ ❛❧❧♦✇ ❢♦r ✐♠♣❡r❢❡❝t✐♦♥s ❛♥❞ s♠❛❧❧
❡rr♦rs ✐♥ ❡❛❝❤ ♠❛t✉r✐t② i✳ a✱ y CDS (t)✱ vt ❛r❡ ❑ ① ✶ ✈❡❝t♦rs✱ zCDS (t, si ) ❛♥❞ A(t, si ) ❛r❡ ▼ ① ✶
✈❡❝t♦rs✱ Φ ✐s ❛ ❑ ① ❑ ❞✐❛❣♦♥❛❧ ♠❛tr✐① ❛♥❞ B(t, si ) ✐s ❛♥ ▼ ① ❑ ♠❛tr✐① ✇❤❡r❡ ❑ ✐s t❤❡ ♥✉♠❜❡r
♦❢ st❛t❡ ✈❛r✐❛❜❧❡s ✭✐♥ ♦✉r ❝❛s❡ ❑❂✶✮ ❛♥❞ ▼ ✐s t❤❡ ♥✉♠❜❡r ♦❢ ♠❛t✉r✐t✐❡s ❝♦♥s✐❞❡r❡❞ ✭✐♥ ♦✉r ❝❛s❡
▼❂✺✮✳ ❙✐♥❝❡ y CDS (t) ❢♦❧❧♦✇s ❛ ❈■❘ ♣r♦❝❡ss✱ ✇❡ ❝❛♥ r❡✇r✐t❡ t❤❡ s②st❡♠ ❛s ❢♦❧❧♦✇s✿
′
y CDS (t) = µ1 (1 − exp(−α1 ∗ △t)) + exp(−α1 ∗ △t) ∗ y CDS (t − 1) + vt
zCDS (t, si ) = −
lnA(t, si ) B(t, si )
+
∗ y CDS (t) + εt
si − t
si − t
✭✷✾✮
✭✸✵✮
✇❤❡r❡ i = 1, ...., 5 r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ♠❛t✉r✐t✐❡s ❝♦♥s✐❞❡r❡❞✳
❚❤❡ ❡rr♦r t❡r♠ vt r❡♣r❡s❡♥ts t❤❡ ✉♥❛♥t✐❝✐♣❛t❡❞ ❝❤❛♥❣❡ ✭♦r ✐♥♥♦✈❛t✐♦♥✮ ✐♥ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡
CDS
y
(t) ❛♥❞ ❤❛s ❛ ❝♦♥❞✐t✐♦♥❛❧ ❡①♣❡❝t❡❞ ♠❡❛♥ ♦❢ ③❡r♦ ❛♥❞ ❝♦♥❞✐t✐♦♥❛❧ ✈❛r✐❛♥❝❡ ❡q✉❛❧ t♦✿
✶✽
Qt =
σ12 ∗
1 − exp(−α1 ∗ △t)
α1
(0.5 ∗ µ1 ∗ (1 − exp(−α1 ∗ △t)) + exp(−α1 ∗ △t) ∗ y CDS (t − 1))
✭✸✶✮
❲❡ ❛❞♦♣t t❤❡ st❛♥❞❛r❞ ❛ss✉♠♣t✐♦♥ ✐♥ ❑❛❧♠❛♥ ✜❧t❡r ❛♥❞ ❛ss✉♠❡ t❤❛t t❤❡r❡ ✐s ♥♦ s❡r✐❛❧ ♦r
❝r♦ss s❡❝t✐♦♥❛❧ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦rs✳ ❚❤✐s s✐♠♣❧❡ str✉❝t✉r❡ ✐s ✐♠♣♦s❡❞
s♦ t❤❛t t❤❡ s❡r✐❛❧ ❛♥❞ ❝r♦ss s❡❝t✐♦♥❛❧ ❝♦rr❡❧❛t✐♦♥ ♦❢ zCDS (t, si ) ✐s ❛ttr✐❜✉t❡❞ t♦ t❤❡ ✈❛r✐❛t✐♦♥
♦❢ t❤❡ ✉♥♦❜s❡r✈❛❜❧❡ st❛t❡ ✈❛r✐❛❜❧❡ y CDS (t)✳ ❚❤❡r❡❢♦r❡✱ ✇❡ ❝❛♥ ✇r✐t❡ t❤❡ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① ❛s
❢♦❧❧♦✇s✿
vt
Et−1
εt
!
vt
εt
!′
=
Qt
0
0
U
!
✭✸✷✮
✇❤❡r❡ Qt ❛♥❞ U r❡♣r❡s❡♥t t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ✈❛r✐❛♥❝❡ ♦❢ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ ❛♥❞ t❤❡ ✈❛r✐❛♥❝❡s
♦❢ t❤❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦rs ❢♦r ❛❧❧ ♠❛t✉r✐t✐❡s ✭✐✳❡✳ ✶②✱ ✸②✱ ✺②✱ ✼② ❛♥❞ ✶✵②✮ ♦♥ t❤❡ ❞✐❛❣♦♥❛❧
r❡s♣❡❝t✐✈❡❧②✳
✽✳✷
◗✉❛s✐ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞ ✭◗▼▲✮ ❊st✐♠❛t✐♦♥✿
❚❤❡ ✜①❡❞ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ st❛t❡ s♣❛❝❡ r❡♣r❡s❡♥t❛t✐♦♥ ❞❡s❝r✐❜❡❞ ❛❜♦✈❡ ❛r❡ t②♣✐❝❛❧❧② ❡s✲
t✐♠❛t❡❞ ✉s✐♥❣ t❤❡ ♠❛①✐♠✉♠ ❧✐❦❡❧✐❤♦♦❞ ♠❡t❤♦❞✳ ■♥ ♦✉r ❝❛s❡✱ ✇❡ ❛ss✉♠❡ t❤❛t y CDS (t) ❛♥❞
y bond (t) ❛r❡ ❢♦❧❧♦✇✐♥❣ ❛ ❈■❘ ♣r♦❝❡ss✱ t❤❡r❡❢♦r❡ t❤❡ ✐♥♥♦✈❛t✐♦♥s ♦❢ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡s ❛r❡ ♥♦t
♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ✇❤✐❝❤ ♠❛❦❡ t❤❡ st❛♥❞❛r❞ ❧✐♥❡❛r ❑❛❧♠❛♥ ✜❧t❡r ❛ ❜✐❛s❡❞ ❡st✐♠❛t♦r ♦❢ t❤❡
✉♥♦❜s❡r✈❛❜❧❡ st❛t❡ ✈❛r✐❛❜❧❡s✳ ❍♦✇❡✈❡r✱ ❉❡ ❏♦♥❣ ✭✷✵✵✵✮ ❛♥❞ ❈❤❡♥ ❛♥❞ ❙❝♦tt ✭✷✵✵✸✮ ♣❡r❢♦r♠ ❛
▼♦♥t❡✲❈❛r❧♦ ❡①❡r❝✐s❡ ❛♥❞ s❤♦✇ t❤❛t t❤❡r❡ ✐s ♥♦ ❡✈✐❞❡♥❝❡ ♦❢ s✐❣♥✐✜❝❛♥t ❜✐❛s ✐♥ t❤❡ ♣❛r❛♠❡t❡r
❡st✐♠❛t❡s✳ ❚❤❡r❡❢♦r❡✱ ❜② ✉s✐♥❣ t❤❡ ◗▼▲ ❡st✐♠❛t♦r t❤❡ ❛✉t❤♦rs ♣r♦✈❡ t❤❛t ✐t ✐s ♣♦ss✐❜❧❡ t♦
♦❜t❛✐♥ ❝♦♥s✐st❡♥t ❡st✐♠❛t♦rs✳ ❲❡ ❢♦❧❧♦✇ t❤❡✐r ❛♣♣r♦❛❝❤ ❛♥❞ ❡st✐♠❛t❡ t❤❡ ♣❛r❛♠❡t❡rs ✉s✐♥❣ t❤❡
◗▼▲ ❛s ❢♦❧❧♦✇s✿
maxθ lnl =
T
X
lt =
t=1
T
X
′
−0.5 ∗ (ln | Ht | +ut ∗ Ht−1 ∗ ut )
✭✸✸✮
t=1
✇❤❡r❡ θ r❡♣r❡s❡♥ts t❤❡ ✈❡❝t♦r ♦❢ ♣❛r❛♠❡t❡rs t♦ ♦♣t✐♠✐③❡ θ = (α1 , µ1 , σ1 , λ1 , ε1 (1), ε1 (3), ε1 (5), ε1 (7), ε1 (10))
❛♥❞ ut ✭t❤❡ ✐♥♥♦✈❛t✐♦♥s ♦❢ zCDS (t, si )✮ ✐s ❞❡✜♥❡❞ ❛s ❢♦❧❧♦✇s✿
ut = zCDS (t, si ) − (−
lnA(t, si ) B(t, si )
ˆ − 1)))
+
∗ (a + Φ ∗ y CDS (t
si − t
si − t
✶✾
✭✸✹✮
ˆ − 1) ✐s ❛♥ ❡st✐♠❛t❡ ♦❢ y CDS (t − 1) ❜❛s❡❞ ♦♥ u
ˆ − 2)✳ ❚❤❡
CDS (t
✇❤❡r❡ y CDS (t
t−2 ❛♥❞ y
❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① Ht ✐s ❞❡✜♥❡❞ ❛s ❢♦❧❧♦✇s✿
✭✸✺✮
′
Ht = E(ut ∗ ut )
❚❤❡ ❡st✐♠❛t✐♦♥ ✐s ❛❝❤✐❡✈❡❞ ❜② ❝❛❧❝✉❧❛t✐♥❣ r❡❝✉rs✐✈❡❧② t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡
❝♦♥❞✐t✐♦♥❛❧ ♦♥ t❤❡ ♦❜s❡r✈❛t✐♦♥s ❛t t✐♠❡ t✳ ❲❡ st❛rt t❤❡ r❡❝✉rs✐♦♥ ❜② ❛ss✉♠✐♥❣ t❤❛t
t❤❡ ✐♥✐t✐❛❧ ✈❛❧✉❡s ❛t t✐♠❡ ③❡r♦ ♦❢ y CDS (0) ❛♥❞ H0 ❛r❡ ❡q✉❛❧ t♦ t❤❡ ✉♥❝♦♥❞✐t✐♦♥❛❧ ♠❡❛♥ µ1 ❛♥❞
2
∗(σ1 )
✈❛r✐❛♥❝❡ µ12∗α
r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ❑❛❧♠❛♥ ✜❧t❡r ❛❧❣♦r✐t❤♠ ❝♦♥s✐sts ♦❢ t❤r❡❡ ✐♠♣♦rt❛♥t st❡♣s✿
1
♣r❡❞✐❝t✐♦♥✱ ✉♣❞❛t✐♥❣ ❛♥❞ ❡st✐♠❛t✐♦♥✳ ■♥ ♦r❞❡r t♦ ❡st✐♠❛t❡ t❤❡ ♣❛r❛♠❡t❡r ✈❡❝t♦r θ✱ ❛ ❣♦♦❞
✐♥✐t✐❛❧ ❣✉❡ss ✐s ♦❢ ❛ ❦❡② ✐♠♣♦rt❛♥❝❡✳ ❚❤❡r❡❢♦r❡✱ ✇❡ tr② ❞✐✛❡r❡♥t ✐♥✐t✐❛❧ ✈❛❧✉❡s✷✶ ✉♥t✐❧ ✇❡ r❡❛❝❤
t❤❡ ❣❧♦❜❛❧ ♠❛①✐♠✉♠ ❛♥❞ ✇❡ ❡st✐♠❛t❡ t❤❡ st❛♥❞❛r❞ ❡rr♦rs ✉s✐♥❣ t❤❡ ❲❤✐t❡ ♠❡t❤♦❞ ✭❲❤✐t❡✱
✶✾✽✷✮✳
❋♦r ❛ ♠♦r❡ ❞❡t❛✐❧❡❞ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❑❛❧♠❛♥ ✜❧t❡r ❡st✐♠❛t✐♦♥ ❛♣♣❧✐❡❞ t♦ t❤❡ ❈■❘ ♣r♦❝❡ss✱
✇❡ r❡❢❡r t♦ ❉❡ ❏♦♥❣ ✭✷✵✵✵✮ ❛♥❞ ❈❤❡♥ ❛♥❞ ❙❝♦tt ✭✷✵✵✸✮✳
y CDS (t)
✽✳✸
❑❛❧♠❛♥ ❋✐❧t❡r ❘❡s✉❧ts✿
■♥ t❤❡ ❢♦❧❧♦✇✐♥❣✱ ✇❡ ♣r❡s❡♥t t❤❡ ❡st✐♠❛t✐♦♥ r❡s✉❧ts ♦❢ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ λ1
❛♥❞ t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ λ2 ✳
✽✳✸✳✶
❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ Pr❡♠✐✉♠✿
❚❛❜❧❡ ✺ ✐♥❞✐❝❛t❡s t❤❛t ❛❧❧ ❡st✐♠❛t❡❞ ♣❛r❛♠❡t❡rs s❤♦✇ str♦♥❣ s✐❣♥✐✜❝❛♥❝❡ ✐♥ t❤❡ s❡♥s❡ t❤❛t
t❤❡ ❡st✐♠❛t❡❞ ✈❛❧✉❡s ❛r❡ ❛ ❧♦t ❤✐❣❤❡r t❤❛♥ t❤❡✐r st❛♥❞❛r❞ ❡rr♦rs✳ ❚❤❡ t❛❜❧❡ ❛❧s♦ ✐♥❞✐❝❛t❡s
t❤❛t t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ λ1 ✐s str♦♥❣❧② s✐❣♥✐✜❝❛♥t ❞✉r✐♥❣ ❜♦t❤ t❤❡ ♣r❡✲❝r✐s✐s ❛♥❞ ❝r✐s✐s
♣❡r✐♦❞s✳ ❋♦r ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡②✱ λ1 ✐s ❤✐❣❤❡r ❞✉r✐♥❣ t❤❡ ♣r❡✲❝r✐s✐s t❤❛♥ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✱
❤♦✇❡✈❡r P❤✐❧✐♣♣✐♥❡s s❤♦✇s t❤❡ ♦♣♣♦s✐t❡ r❡s✉❧ts ❛s λ1 ✐s ❤✐❣❤❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✳ ❚❤❡
✈♦❧❛t✐❧✐t② ♣❛r❛♠❡t❡rs✱ ❛❧t❤♦✉❣❤ s✐❣♥✐✜❝❛♥t ❞✉r✐♥❣ ❛❧❧ ♣❡r✐♦❞s✱ ❛r❡ ❤✐❣❤❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s t❤❛♥
t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞✱ t❤✐s ✐s ✐♥ ❧✐♥❡ ✇✐t❤ t❤❡ ❤✐❣❤❡r ✈♦❧❛t✐❧✐t② ❡①♣❡r✐❡♥❝❡❞ ❞✉r✐♥❣ ❝r✐s✐s t✐♠❡✳
❙❡❝♦♥❞❧②✱ ❚❛❜❧❡ ✺ s❤♦✇s t❤❛t t❤❡ ❤❛❧❢ ❧✐❢❡✷✷ ✐s s❤♦rt❡r ❞✉r✐♥❣ t❤❡ ♣r❡✲❝r✐s✐s t✐♠❡ ❢♦r P❤✐❧✐♣♣✐♥❡s
❛♥❞ ❧♦♥❣❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s t✐♠❡ ❢♦r ❜♦t❤ ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡② ✇❤✐❝❤ ♠❡❛♥ t❤❛t P❤✐❧✐♣♣✐♥❡s ❤❛s
str♦♥❣❡r ♠❡❛♥ r❡✈❡rs✐♦♥ ❞✉r✐♥❣ t❤❡ ♣r❡✲❝r✐s✐s t✐♠❡ ❛♥❞ ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡② ❤❛✈❡ str♦♥❣❡r ♠❡❛♥
r❡✈❡rs✐♦♥ ❞✉r✐♥❣ ❝r✐s✐s t✐♠❡✳
❋✉rt❤❡r♠♦r❡✱ ❢♦r ❛❧❧ ❝♦✉♥tr✐❡s ❛♥❞ ❞✉r✐♥❣ ❜♦t❤ t❤❡ ♣r❡ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s✱ t❤❡ ♣r✐❝✐♥❣
❡rr♦rs ❢♦r t❤❡ ♦♥❡ ②❡❛r ♠❛t✉r✐t② ✭✐✳❡✳ ε1 (1)✮ ❛r❡ ❧❛r❣❡r t❤❛♥ t❤♦s❡ ♦❢ t❤❡ ♦t❤❡r ♠❛t✉r✐t✐❡s
✷✶
❲❡ ✉s❡ t❤❡ ❢✉♥❝t✐♦♥ ❈r❡❛t❡❖♣t✐♠Pr♦❜❧❡♠ ✐♥ ▼❛t❧❛❜ ❝♦♠❜✐♥❡❞ ✇✐t❤ ❢♠✐♥❝♦♥✳
❈r❡❛t❡❖♣t✐♠Pr♦❜❧❡♠ ✐♥
▼❛t❧❛❜ ❡♥❛❜❧❡s ✉s t♦ t❡st t❤♦✉s❛♥❞s ♦❢ ✐♥✐t✐❛❧ ❣✉❡ss❡s ❛♥❞ ♣✐❝❦ t❤❡ ❜❡st ❡st✐♠❛t❡s✳
✷✷
❚❤❡ ❤❛❧❢ ❧✐❢❡ ❣✐✈❡s t❤❡ s❧♦✇♥❡ss ♦❢ ♠❡❛♥ r❡✈❡rs✐♦♥ ♣r♦❝❡ss ❛♥❞ ✐s ❝♦♠♣✉t❡❞ ❛s ❢♦❧❧♦✇s✿
✷✵
t = −ln(0.5)/α
✇❤✐❝❤ ✐♥❞✐❝❛t❡ t❤❛t t❤❡ ♠♦❞❡❧ ✜ts ❜❡tt❡r ❧♦♥❣❡r ♠❛t✉r✐t✐❡s✳ ❚❤✐s r❡s✉❧t ✐s ✐♥ ❧✐♥❡ ✇✐t❤ P❛♥
❛♥❞ ❙✐♥❣❧❡t♦♥ ✭✷✵✵✽✮ ✇❤♦ ❡♠♣❤❛s✐③❡ t❤❛t t❤❡r❡ ❛r❡ s♦♠❡ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ s❤♦rt ❡♥❞ ♦❢ ❈❉❙
❝✉r✈❡ t❤❛t ❛r❡ ♥♦t ✇❡❧❧ ❝❛♣t✉r❡❞ ❜② t❤❡ ♦♥❡ ❢❛❝t♦r ♠♦❞❡❧✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ t❤❡
♣r✐❝✐♥❣ ❡rr♦rs ❛❝r♦ss ❛❧❧ ♠❛t✉r✐t✐❡s ❛r❡ ❤✐❣❤❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞ ✇❤✐❝❤ ✐♠♣❧② t❤❡ ❞✐✣❝✉❧t②
♦❢ ✜tt✐♥❣ ❛ ❤✐❣❤❧② ✈♦❧❛t✐❧❡ t✐♠❡ s❡r✐❡s✳
■♥ ♦✉r ♠♦❞❡❧✱ ✇❡ ❛ss✉♠❡❞ t❤❛t ❧✐q✉✐❞✐t② r✐s❦ ❡♥t❡rs ♦♥❧② t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❧❡❣ ♦❢ t❤❡ ❈❉❙
❝♦♥tr❛❝t ✇❤✐❝❤ ♠❡❛♥s t❤❛t t❤❡ ♣r♦t❡❝t✐♦♥ ❜✉②❡r ✇✐❧❧ ♣❛② ❛ ❧♦✇❡r ♣r✐❝❡ ✐❢ t❤❡ ❈❉❙ ♠❛r❦❡t
✐s ✐❧❧✐q✉✐❞✷✸ ✱ t❤✐s ✐s ❡q✉✐✈❛❧❡♥t t♦ s❛② t❤❛t t❤❡ ♣r♦t❡❝t✐♦♥ ❜✉②❡r ✇✐❧❧ ❡❛r♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠✷✹ ✳ ❚❛❜❧❡ ✺ r❡✈❡❛❧s t❤❛t t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✐s ♣♦s✐t✐✈❡ ❛♥❞ s✐❣♥✐✜❝❛♥t ❢♦r
❛❧❧ t❤❡ ❝♦✉♥tr✐❡s✱ t❤✐s ✐♥❞✐❝❛t❡s t❤❛t t❤❡ ♣r✐❝❡ ♦❢ ❧✐q✉✐❞✐t② r✐s❦ ❤❛s s✐❣♥✐✜❝❛♥t ✐♠♣❛❝t ♦♥ t❤❡
❞❡❢❛✉t❧❛❜❧❡ ❧❡❣ ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝t ❛♥❞ ❞♦❡s r❡❞✉❝❡ ❈❉❙ s♣r❡❛❞s ✐♥ ❧✐♥❡ ✇✐t❤ ♦✉r ♠♦❞❡❧
❛ss✉♠♣t✐♦♥✳ ❍♦✇❡✈❡r✱ t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❞✐✛❡rs ❞❡♣❡♥❞✐♥❣ ♦♥ ♠❛r❦❡t
❝♦♥❞✐t✐♦♥s✳ ❋♦r ✐♥st❛♥❝❡✱ ❢♦r t❤❡ ❝❛s❡ ♦❢ ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡② t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠ ❞❡❝r❡❛s❡s ❞✉r✐♥❣ t❤❡ ❝r✐s✐s ✇❤✐❝❤ ♠❛② ♠❡❛♥ t❤❛t t❤❡ ❈❉❙ ♠❛r❦❡t ✐s ♠♦r❡ ❧✐q✉✐❞
❞✉r✐♥❣ ❝r✐s✐s t✐♠❡✳ ❍♦✇❡✈❡r✱ ❢♦r t❤❡ ❝❛s❡ ♦❢ P❤✐❧✐♣♣✐♥❡s✱ t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠ ✐♥❝r❡❛s❡s ✇❤✐❝❤ ♠❛② ✐♠♣❧② t❤❛t t❤❡ ❈❉❙ ♠❛r❦❡t ✐s ♠♦r❡ ✐❧❧✐q✉✐❞ ❞✉r✐♥❣ ❝r✐s✐s t✐♠❡✳
✽✳✸✳✷
❇♦♥❞ ▲✐q✉✐❞✐t② ❘✐s❦ Pr❡♠✐✉♠✿
❙✐♠✐❧❛r❧② t♦ t❤❡ ❈❉❙ ♠❛r❦❡t✱ ✇❡ t❡st ❢♦r t❤❡ ♣r❡s❡♥❝❡ ♦❢ t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠✳
❚❛❜❧❡ ✻ s❤♦✇s t❤❛t t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ λ2 ✐s s✐❣♥✐✜❝❛♥t ❛t ✶✪ ❧❡✈❡❧ ❞✉r✐♥❣ ❜♦t❤
t❤❡ ♣r❡ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s ❛♥❞ ❛❝r♦ss ❛❧❧ ❝♦✉♥tr✐❡s✳ ❚❤❡ r❡s✉❧ts ✐♥❞✐❝❛t❡ t❤❛t t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢
λ2 ✐s ❤✐❣❤❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞ ❢♦r ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡② ✭✇❤✐❝❤ ✐s t❤❡ ♦♣♣♦s✐t❡ ♦❢ t❤❡ ❈❉❙
❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ λ1 ✮✳ P❤✐❧❧✐♣✐♥❡s ❞✐s♣❧❛②s ❛ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ t❤❛t ✐s r♦✉❣❤❧②
♦❢ s✐♠✐❧❛r ♠❛❣♥✐t✉❞❡ ❛❝r♦ss ❜♦t❤ t❤❡ ♣r❡ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s✳ ❋✉rt❤❡r♠♦r❡✱ ❚❛❜❧❡ ✻ ✐♥❞✐❝❛t❡s
t❤❛t t❤❡ ❤❛❧❢ ❧✐❢❡ ✐s ❧♦✇❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s t✐♠❡ ❢♦r P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❞✉r✐♥❣ t❤❡ ♣r❡✲❝r✐s✐s t✐♠❡
❢♦r ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡② ✇❤✐❝❤ ✐s ❛❧s♦ t❤❡ ♦♣♣♦s✐t❡ ♦❢ ✇❤❛t ❤❛s ❜❡❡♥ ❢♦✉♥❞ ❢♦r t❤❡ ❈❉❙ ♠❛r❦❡t✳
❲❤✐❧❡ ✈♦❧❛t✐❧✐t② ♣❛r❛♠❡t❡rs ✭σ ✮ ❛r❡ ❤✐❣❤❡r ❞✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞ ❢♦r t❤❡ ❈❉❙ ♠❛r❦❡t✱
t❤❡ ❜♦♥❞ ♠❛r❦❡t ❞♦❡s ♥♦t s❤♦✇ s✉❝❤ ❛ ❝❧❡❛r ♣✐❝t✉r❡ ❛s ❇r❛③✐❧ ❛♥❞ P❤✐❧✐♣♣✐♥❡s ❤❛✈❡ ❤✐❣❤❡r
✈♦❧❛t✐❧✐t② ❞✉r✐♥❣ t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞✱ ❤♦✇❡✈❡r ❚✉r❦❡② ❤❛s ❤✐❣❤❡r ✈♦❧❛t✐❧✐t② ❞✉r✐♥❣ ❝r✐s✐s t✐♠❡✳
❋✉rt❤❡r♠♦r❡✱ ✐♥ t❤❡ ❈❉❙ ♠❛r❦❡t✱ t❤❡ ❤✐❣❤❡st ♣r✐❝✐♥❣ ❡rr♦rs ❛r❡ ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ♦♥❡ ②❡❛r
♠❛t✉r✐t② ❢♦r ❛❧❧ ❝♦✉♥tr✐❡s✱ s✉❝❤ ❛ ❝❧❡❛r ♣❛tt❡r♥ ❞♦❡s ♥♦t ♠❛♥✐❢❡st ✐ts❡❧❢ ✐♥ t❤❡ ❜♦♥❞ ♠❛r❦❡t✳
❈❧❡❛r❧②✱ t❤❡ ❡st✐♠❛t❡❞ ♣❛r❛♠❡t❡rs ❤✐❣❤❧✐❣❤t t❤❡ ❤❡t❡r♦❣❡♥❡✐t② ✐♥ ❧✐q✉✐❞✐t② r✐s❦ ❜❡t✇❡❡♥ ❈❉❙
❛♥❞ ❜♦♥❞ ♠❛r❦❡ts✳ ■♥❞❡❡❞✱ ❢♦r ❡❛❝❤ ❝♦✉♥tr②✱ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❜❡❤❛✈❡ ❞✐✛❡r❡♥t❧② ❛s
✷✸
■❢ t❤❡ ❈❉❙ s❡❧❧❡rs s❡❧❧ ❛♥ ✐❧❧✐q✉✐❞ ♣r♦t❡❝t✐♦♥ t♦ t❤❡ ♣r♦t❡❝t✐♦♥ ❜✉②❡r✱ t❤❡ ❧❛tt❡r ✇✐❧❧ ✐♥❝✉r ❝♦sts ✐❢ ❤❡ ❞❡❝✐❞❡s
t♦ tr❛❞❡ ✐t✱ ❤❡ ✇✐❧❧ t❤❡r❡❢♦r❡ r❡q✉✐r❡ ❛ ❞✐s❝♦✉♥t ❛s ❛ ❝♦♠♣❡♥s❛t✐♦♥ ❢♦r t❤❛t✳
✷✹
❚❤✐s ❛ss✉♠♣t✐♦♥ ✐s ❞✐✛❡r❡♥t ❢r♦♠ t❤❛t ♦❢ ❇✉❤❧❡r ❛♥❞ ❚r❛♣♣ ✭✷✵✶✵✮ ✇❤❡r❡ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❡♥t❡rs
❜♦t❤ t❤❡ ❞❡❢❛✉❧t❛❜❧❡ ❛♥❞ t❤❡ ♣r❡♠✐✉♠ ❧❡❣s ♦❢ t❤❡ ❈❉❙ ❝♦♥tr❛❝t✳
✷✶
t❤❡② ❤❛✈❡ ❞✐✛❡r❡♥t ✈♦❧❛t✐❧✐t② ❧❡✈❡❧s ❛♥❞ ♠❡❛♥✲r❡✈❡rs✐♦♥ s♣❡❡❞s✳ ■♥ t❤❡ ♥❡①t s❡❝t✐♦♥✱ ✇❡ st✉❞②
t❤❡ ❧❡❛❞✲❧❛❣ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠✳
✾ ❇♦♥❞ ❛♥❞ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ Pr❡♠✐✉♠✿
✾✳✶
❉❡s❝r✐♣t✐✈❡ ❙t❛t✐st✐❝s✿
■♥ t❤✐s s❡❝t✐♦♥✱ ✇❡ ❡①tr❛❝t t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❢❛❝t♦r ✈❛❧✉❡s ♦r st❛t❡ ✈❛r✐❛❜❧❡s ✭y CDS (t) ❛♥❞
y bond (t)✮ ❢♦r ❛❧❧ t ❢r♦♠ t❤❡ ❑❛❧♠❛♥ ✜❧t❡r ❡st✐♠❛t✐♦♥ ❢♦r ❜♦t❤ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts r❡s♣❡❝✲
t✐✈❡❧② ❛♥❞ ♠✉❧t✐♣❧② t❤❡♠ ✇✐t❤ t❤❡✐r r❡s♣❡❝t✐✈❡ ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦ ✭λ1 ❛♥❞ λ2 ✮ ✐♥ ♦r❞❡r t♦
r❡tr✐❡✈❡ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✭y CDS (t) ∗ λ1 ❛♥❞ y bond (t) ∗ λ2 ✮ ❢♦r ❜♦t❤ ♠❛r✲
❦❡ts✳ ■♥ ❋✐❣✉r❡s ✼ ❛♥❞ ✽✱ ✇❡ ♣❧♦t t❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠ ❢♦r ❡❛❝❤ ❝♦✉♥tr② ❛♥❞ ❢♦r ❜♦t❤ t❤❡ ♣r❡ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞ r❡s♣❡❝t✐✈❡❧②✳ ❇♦t❤ ✜❣✉r❡s
❝❧❡❛r❧② ❤✐❣❤❧✐❣❤t t❤❡ ❞✐✛❡r❡♥❝❡s t❤❛t ❡①✐st ❜❡t✇❡❡♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r♦♣❡rt✐❡s ❢♦r ❡❛❝❤ ♠❛r❦❡t✳
❆s ❛ s❡❝♦♥❞ st❡♣✱ ✇❡ ❛❧s♦ st✉❞② t❤❡ ❞❡s❝r✐♣t✐✈❡ st❛t✐st✐❝s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❜♦♥❞ ❛♥❞ ❈❉❙
❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥❣❡s✳ ❚❛❜❧❡ ✼ ♣r❡s❡♥ts ❛ ❝♦♠♣❛r❛t✐✈❡ ❛♥❛❧②s✐s ❜❡t✇❡❡♥ t❤❡ ❝❤❛♥❣❡s
♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❢♦r ❜♦t❤ t❤❡ ♣r❡ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s✳
❚❤❡ t❛❜❧❡ r❡✈❡❛❧s t❤❛t ✇❤❡♥ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥❣❡s ❛r❡ ❧♦✇ ✭✐✳❡✳
❧♦✇ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ❛♥❞ ❧♦✇ ♠❡❛♥✮✱ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥❣❡s
❡①❤✐❜✐t ❤✐❣❤❡r st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ❛♥❞ ❤✐❣❤❡r ♠❡❛♥ ✭❛♥❞ ✈✐❝❡ ✈❡rs❛✮✳ ❚❤✐s r❡❧❛t✐♦♥s❤✐♣ ♠❛②
❜❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ ❢❛❝t t❤❛t ❜♦t❤ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts ❛r❡ s✉❜st✐t✉t❡ t♦ ❡❛❝❤ ♦t❤❡r✳
❲❤❡♥ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❤✐❣❤✱ ✐♥✈❡st♦rs ✐♥✈❡st ✐♥ t❤❡ ❜♦♥❞ ♠❛r❦❡t✳ ❍♦✇❡✈❡r✱ ✇❤❡♥ ❜♦♥❞
❧✐q✉✐❞✐t② r✐s❦ ✐s ❤✐❣❤✱ t❤❡r❡ ✐s ❛ ❞❡❝r❡❛s❡ ✐♥ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✇❤✐❝❤ ✐♠♣❧② t❤❛t ✐♥✈❡st♦rs
tr❛❞❡ ❝r❡❞✐t r✐s❦ ♠♦st❧② ✐♥ t❤❡ ❈❉❙ ♠❛r❦❡t✳ ❚❤✐s ♦♣♣♦s✐t❡ r❡❧❛t✐♦♥s❤✐♣ ✐s ❛❧s♦ ❝♦♥s✐st❡♥t ✇✐t❤
s♦♠❡ ♣❛r❛♠❡t❡r ✈❛❧✉❡s ❡st✐♠❛t❡❞ ✐♥ s❡❝t✐♦♥ ✽ ✇❤❡r❡ ✇❡ ✜♥❞ t❤❛t ❜♦t❤ ♠❛r❦❡ts ❤❛✈❡ ♦♣♣♦s✐t❡
♠❡❛♥✲✈❡rs✐♦♥ s♣❡❡❞✳
■♥ ♦✉r ♠♦❞❡❧✱ ✇❡ ❛ss✉♠❡❞ t❤❛t ❈❉❙ ❜✉②❡rs ❡❛r♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠✳ ■♥t✉✐t✐✈❡❧②✱
✇❤❡♥ t❤❡ ❈❉❙ ♠❛r❦❡t ✐s ✐❧❧✐q✉✐❞✱ ❈❉❙ ❜✉②❡rs r❡q✉✐r❡ ❛ ❞✐s❝♦✉♥t ✭❜② ❞❡❝r❡❛s✐♥❣ t❤❡ ❛s❦ q✉♦t❡✮
✐♥ ♦r❞❡r t♦ ❜✉② ❛ ♣r♦t❡❝t✐♦♥✳ ■❢ t❤❡ ♣r❡♠✐✉♠ r❡q✉✐r❡❞ ❜② ❈❉❙ ❜✉②❡rs ✐s t♦♦ ❤✐❣❤✱ ❈❉❙ s❡❧❧❡rs
♠❛② ♣r❡❢❡r t♦ ❜✉② ❝r❡❞✐t r✐s❦ ✐♥ t❤❡ ❜♦♥❞ ♠❛r❦❡t ❜❡❝❛✉s❡ ✐t ❤❛s ❛ ❧♦✇❡r ❧✐q✉✐❞✐t② r✐s❦✳ ❖✈❡r❛❧❧
♦✉r r❡s✉❧ts ✐♠♣❧② t❤❛t ✐♥✈❡st♦rs tr❛❞❡ ❝r❡❞✐t r✐s❦ ✐♥ t❤❡ ♠❛r❦❡t ✇❤❡r❡ t❤❡r❡ ✐s ❛ ❧♦✇❡r ❧✐q✉✐❞✐t②
r✐s❦✳
✷✷
✾✳✷
●r❛♥❣❡r✲❈❛✉s❛❧✐t② ❆♥❛❧②s✐s✿
❆s ❛ ❢✉rt❤❡r st❡♣✱ ✇❡ st✉❞② ✇❤❡t❤❡r t❤❡r❡ ❡①✐sts ❛♥② t❡♠♣♦r❛❧ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ t❤❡ t✐♠❡✲
✈❛r②✐♥❣ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥❣❡s✳ ❚♦ ❡①❛♠✐♥❡ t❤✐s ✇❡ ❝❛♥ t❡st ❢♦r t❤❡
♣r❡s❡♥❝❡ ♦❢ ●r❛♥❣❡r ❝❛✉s❛❧✐t②✳ ❆ ●r❛♥❣❡r ❝❛✉s❛❧✐t② t❡st ✐s ❛ ♣♦✇❡r❢✉❧ ✐♥❞✐❝❛t♦r ♦❢ ❝❛✉s❛❧✐t②
❛s ✐t ❞❡t❡r♠✐♥❡s ✇❤❡t❤❡r t❤❡r❡ ✐s ❛ ✢♦✇ ♦❢ ✐♥❢♦r♠❛t✐♦♥ ❢r♦♠ ♦♥❡ ✈❛r✐❛❜❧❡ t♦ ❛♥♦t❤❡r✱ ❛♥❞ t❤❡
❞✐r❡❝t✐♦♥ ✐♥ ✇❤✐❝❤ ✐t tr❛✈❡❧s✳ ❍♦✇❡✈❡r✱ ❜❡❢♦r❡ ❡①❛♠✐♥✐♥❣ ●r❛♥❣❡r ❝❛✉s❛❧✐t② ✇❡ ♠✉st ❞❡t❡r♠✐♥❡
✇❤❡t❤❡r ♦r ♥♦t t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❧❡✈❡❧s ❛r❡ ❝♦✲✐♥t❡❣r❛t❡❞✳
❖✉r ❛♥❛❧②s✐s r❡✈❡❛❧s t❤❛t ❜♦t❤ ♣r❡♠✐✉♠ ❛r❡ ♥♦t ❝♦✐♥t❡❣r❛t❡❞✱ t❤✐s ✐s t♦ ❜❡ ❡①♣❡❝t❡❞ ❜❡❝❛✉s❡✱
❛s ✇❡ ❞♦❝✉♠❡♥t❡❞ ❛❜♦✈❡✱ t❤❡r❡ ✐s ❛ s✉❜st❛♥t✐❛❧ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r♦♣❡rt✐❡s
♦❢ ❡❛❝❤ ♠❛r❦❡t✳ ❲❡ t❤✉s ♣r♦❝❡❡❞ t♦ ♣❡r❢♦r♠ t❤❡ ●r❛♥❣❡r ❝❛✉s❛❧✐t② t❡st ✐♥ ♦r❞❡r t♦ t❡st ❢♦r
✐♥❢♦r♠❛t✐♦♥ ✢♦✇ ❢r♦♠ ❜♦t❤ ❞✐r❡❝t✐♦♥s ✭✐✳❡✳ ❈❉❙ t♦ ❜♦♥❞s ❛♥❞ ✈✐❝❡ ✈❡rs❛✮✳ ■♥ ❛❧❧ ♦♣t✐♠✐s❛t✐♦♥s
✇❡ ❛❧❧♦✇❡❞ ❢♦r ❛ ♠❛①✐♠✉♠ ❧❛❣ ♦❢ ✸ ❞❛②s ✐♥ ♦r❞❡r t♦ s❤♦✇ t❤❡ ♣❡rs✐st❡♥❝❡ ♦❢ t❤❡ ✐♥❢♦r♠❛t✐♦♥
✢♦✇✳ ❚❤❡ ♠♦❞❡❧ ❡q✉❛t✐♦♥ ✐s✿
△ACDS (t) =
Pm
i=1 αi
∗ △ACDS (t − 1) +
Pm
i=1 βi
∗ △ABond (t − 1) + εi
✭✸✻✮
❲❤❡r❡ ACDS (t) = y CDS (t) ∗ λ1 ❛♥❞ Abond (t) = y bond (t) ∗ λ2 ✳ ❲❡ t❤❡♥ t❡st t❤❡ ♥✉❧❧
❤②♣♦t❤❡s✐s ✇❤✐❝❤ ✐s t❤❛t t❤❡ ❧❛❣❣❡❞ ✈❛❧✉❡s ♦❢ △ABond (t − 1) ❞♦ ♥♦t ●r❛♥❣❡r ❝❛✉s❡ △ACDS (t)✳
❋♦r♠❛❧❧②✱ t❤✐s ✐s t❤❡ t❡st t❤❛t β = 0✳ ❆ ❞❡✈✐❛t✐♦♥ ❢r♦♠ t❤✐s ❡q✉❛❧✐t② ✇✐t❤ st❛t✐st✐❝❛❧ s✐❣♥✐✜❝❛♥❝❡
❛s ♠❡❛s✉r❡❞ ✉s✐♥❣ ❛♥ ❋✲st❛t✐st✐❝ ❛❧❧♦✇s ✉s t♦ ❛❝❝❡♣t ♦r r❡❥❡❝t t❤❡ ♥✉❧❧ ❤②♣♦t❤❡s✐s✳ ❲❡ s❡t ❛
s✐❣♥✐✜❝❛♥❝❡ ❧❡✈❡❧ ♦❢ ✵✳✶✪ ❢♦r r❡❥❡❝t✐♦♥ ♦❢ t❤❡ ❤②♣♦t❤❡s❡s✳ ❲❡ t❤❡♥ r❡♣❡❛t❡❞ t❤✐s ❡①❡r❝✐s❡ ✐♥
❛♥ ❛tt❡♠♣t t♦ s❡❡ ✐❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥❣❡s ●r❛♥❣❡r ❝❛✉s❡ t❤❡
t✐♠❡✲✈❛r②✐♥❣ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ♣❡♠✐✉♠ ❝❤❛♥❣❡s✳
❚❛❜❧❡ ✽ s❤♦✇s t❤❡ r❡s✉❧ts✳ ❚❤❡ t❛❜❧❡ r❡✈❡❛❧s t❤❛t✱ ❜❡❢♦r❡ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✱ ❢♦r ❇r❛③✐❧ ❛♥❞
❚✉r❦❡② △Abond ❣r❛♥❣❡r ❝❛✉s❡s t❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡ ✈❛r②✐♥❣ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠
(△ACDS ) ♠♦r❡ str♦♥❣❧② t❤❛♥ △ACDS ❣r❛♥❣❡r ❝❛✉s❡s △Abond ✳ ❖♥ ♦♥❡ ❤❛♥❞✱ ❢♦r ❇r❛③✐❧✱ ✇❡
♦❜s❡r✈❡ t❤❛t △Abond ❣r❛♥❣❡r ❝❛✉s❡s △ACDS ✉♣ t♦ ❧❛❣ ✶✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ❚✉r❦❡② s❤♦✇s ❛
❧♦✇❡r s✐❣♥✐✜❝❛♥❝❡ ❧❡✈❡❧ ♦❢ t❤❡ ❣r❛♥❣❡r ❝❛✉s❛❧✐t② ❢r♦♠ △ACDS t♦ △Abond ✳ ❍♦✇❡✈❡r✱ t❤❡ r❡s✉❧ts
♦❢ P❤✐❧✐♣♣✐♥❡s ❢♦r t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞ r❡✈❡❛❧ t❤❛t △ACDS str♦♥❣❧② ❣r❛♥❣❡r ❝❛✉s❡s △Abond
♠♦r❡ t❤❛♥ t❤❡ ♦t❤❡r ✇❛② ❛r♦✉♥❞ ❛s t❤❡ ❋✲st❛t✐st✐❝s ❛r❡ ❛ ❧♦t ❤✐❣❤❡r t❤❛♥ t❤❡✐r ❝r✐t✐❝❛❧ ✈❛❧✉❡s✳
❉✉r✐♥❣ t❤❡ ❝r✐s✐s ♣❡r✐♦❞✱ ✇❡ ♦❜s❡r✈❡ t❤❛t t❤❡ ❧✐q✉✐❞✐t② ✢♦✇ ❜❡t✇❡❡♥ ❜♦t❤ ♠❛r❦❡ts ❝❤❛♥❣❡❞
s✉❜st❛♥t✐❛❧❧②✳ ❋♦r ✐♥st❛♥❝❡✱ ✇❡ ♥♦t✐❝❡ t❤❛t t❤❡r❡ ✐s ♥♦ ❢❡❡❞❜❛❝❦ r❡❧❛t✐♦♥s❤✐♣ ✐♥ P❤✐❧✐♣♣✐♥❡s
✇❤✐❝❤ str♦♥❣❧② ❝♦♥tr❛st t❤❡ r❡s✉❧ts ♦❢ t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞✳ ❍♦✇❡✈❡r✱ ❇r❛③✐❧ ❛♥❞ ❚✉r❦❡② s❤♦✇
❛ ●r❛♥❣❡r ❝❛✉s❛❧✐t② ✐♥ ❜♦t❤ ❞✐r❡❝t✐♦♥s ✇✐t❤ ❛ str♦♥❣❡r ✐♥✢✉❡♥❝❡ ❢r♦♠ t❤❡ ❜♦♥❞ t♦ t❤❡ ❈❉❙
♠❛r❦❡t✳
❲❡ ♥♦t❡ t❤❛t t❤❡ ●r❛♥❣❡r ❝❛✉s❛❧✐t② ♣r❡s❡♥t❡❞ ✐♥ t❤❡ t❛❜❧❡ ✐s s❤♦✇♥ ❢♦r ✉♣ t♦ ✸ ❧❛❣s ✇❤✐❝❤
✷✸
✐♠♣❧② t❤❛t t❤❡ ✐♥❢♦r♠❛t✐♦♥ tr❛♥s❢❡r ❜❡t✇❡❡♥ ❜♦t❤ ♠❛r❦❡ts ✐s ♣❡rs✐st❡♥t ❛♥❞ ❧♦♥❣✲❧✐✈❡❞✳ ■♥ ❢❛❝t✱
❛❧t❤♦✉❣❤ t❤❡ r❡s✉❧ts ♦❢ t❤❡ ●r❛♥❣❡r ❝❛✉s❛❧✐t② t❡st ❛r❡ ♠✐①❡❞ ❛s t❤❡r❡ ✐s ♥♦ ♠❛r❦❡t ❝♦♥s✐st❡♥t❧②
❧❡❛❞✐♥❣ t❤❡ ♦t❤❡r✱ ✇❡ ✜♥❞ str♦♥❣ ❡✈✐❞❡♥❝❡ ♦❢ ❧✐q✉✐❞✐t② ✢♦✇ ❢r♦♠ t❤❡ ❈❉❙ t♦ t❤❡ ❜♦♥❞ ♠❛r❦❡t
❛♥❞ ✈✐❝❡ ✈❡rs❛✳
✶✵ ❈♦♥❝❧✉s✐♦♥
❚❤❡r❡ ✐s ❣r♦✇✐♥❣ ❡✈✐❞❡♥❝❡ t❤❛t ❜♦♥❞ ❛♥❞ ❈❉❙ s♣r❡❛❞s ❛r❡ ❛✛❡❝t❡❞ ❜② ❧✐q✉✐❞✐t② r✐s❦✳ ❍♦✇❡✈❡r✱
t❤❡ q✉❛♥t✐✜❝❛t✐♦♥ ♦❢ ❧✐q✉✐❞✐t② r✐s❦✱ t❤❛t ✐s✱ ❞✐st✐♥❣✉✐s❤✐♥❣ ❜❡t✇❡❡♥ t❤❡ ❞❡❢❛✉❧t✲r❡❧❛t❡❞ ❛♥❞ t❤❡
❧✐q✉✐❞✐t②✲r❡❧❛t❡❞ ❝♦♠♣♦♥❡♥ts✱ r❡♠❛✐♥s ❛ ❝❤❛❧❧❡♥❣✐♥❣ t❛s❦✳ ■♥ t❤✐s ♣❛♣❡r✱ ✇❡ ♣r♦✈✐❞❡ t❤❡ ✜rst
st✉❞② t❤❛t ❛♥❛❧②s❡s t❤❡ ❞②♥❛♠✐❝s ♣r♦♣❡rt✐❡s ♦❢ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ s♣❡❝✐✜❝ t♦ t❤❡ t❡r♠
str✉❝t✉r❡ ♦❢ t❤❡ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞ s♣r❡❛❞s✳ ■♥ ♦r❞❡r t♦ ❝❛rr② ♦✉t t❤✐s ❛♥❛❧②s✐s✱ ✇❡ ❡①t❡♥❞
t❤❡ ✇♦r❦ ♦❢ ❈❤❡♥✱ ❋❛❜♦③③✐✱ ❛♥❞ ❙✈❡r❞❧♦✈❡ ✭✷✵✶✵✮ ❛♥❞ ❛ss✉♠❡ t❤❛t t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡
♠✐❞ ❛♥❞ ❛s❦ q✉♦t❡s ♣r♦✈✐❞❡s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ ❧✐q✉✐❞✐t② r✐s❦✳ ❲❡ ❝❤♦♦s❡ t♦ ❛♣♣❧② ♦✉r
❢r❛♠❡✇♦r❦ t♦ ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✱ t❤r❡❡ ❡♠❡r❣✐♥❣ ❝♦✉♥tr✐❡s ✇✐t❤ ❞✐✛❡r❡♥t ❝r❡❞✐t
❤✐st♦r② ❛♥❞ ❢♦r ✇❤✐❝❤ ❛ ❢✉❧❧ t❡r♠ str✉❝t✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❈❉❙ ❛♥❞ ❜♦♥❞ s♣r❡❛❞s ✐s ❛✈❛✐❧❛❜❧❡✳
❲❡ s❤♦✇✱ ❜② ❛♣♣❧②✐♥❣ t❤❡ ❑❛❧♠❛♥ ✜❧t❡r✱ t❤❛t t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✐s s✐❣♥✐✜❝❛♥t ❢♦r
❜♦t❤ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts ❛♥❞ ✐♥ ❜♦t❤ t❤❡ ♣r❡✲ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s✳ ❋✉rt❤❡r♠♦r❡✱ ♦✉r ✜♥❞✐♥❣s
✐♠♣❧② t❤❛t ❛❧t❤♦✉❣❤ t❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❛r❡ s✉❜st❛♥t✐❛❧❧② ❞✐✛❡r❡♥t
t❤❡r❡ ✐s ❛♥ ✐♠♣♦rt❛♥t ❧✐q✉✐❞✐t② s♣✐❧❧✲♦✈❡r ❜❡t✇❡❡♥ ❜♦t❤ ♠❛r❦❡ts✱ ❛s s❤♦✇♥ ❜② ♦✉r ●r❛♥❣❡r✲
❝❛✉s❛❧✐t② ❛♥❛❧②s✐s✱ ✇❤✐❝❤ ♠❛② s✉❣❣❡st t❤❛t ♥♦ ♠❛r❦❡t ❝♦♥s✐st❡♥t❧② ❧❡❛❞s t❤❡ ♦t❤❡r✳ ❋✐♥❛❧❧②✱
♦✉r r❡s✉❧ts s✉❣❣❡st t❤❛t ❜♦t❤ ❜♦♥❞ ❛♥❞ ❈❉❙ ♠❛r❦❡ts ❛❝t ❛s s✉❜st✐t✉t❡ t♦ ❡❛❝❤ ♦t❤❡r ♥❛♠❡❧②
✇❤❡♥ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❤✐❣❤✱ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✐s ❧♦✇ ❛♥❞ ✈✐❝❡ ✈❡rs❛✳ ❙✉❝❤ ❛ s✉❜st✐t✉t✐♦♥
❡✛❡❝t ✐♠♣❧✐❡s t❤❛t ✇❤❡♥ t❤❡ ❈❉❙ ♠❛r❦❡t ✐s ✐❧❧✐q✉✐❞✱ ❈❉❙ ❜✉②❡rs r❡q✉✐r❡ ❛ ❞✐s❝♦✉♥t ✐♥ ♦r❞❡r t♦
❜✉② ❛ ♣r♦t❡❝t✐♦♥✳ ■❢ t❤❡ ♣r❡♠✐✉♠ r❡q✉✐r❡❞ ✐s t♦♦ ❤✐❣❤✱ ❈❉❙ s❡❧❧❡rs ♠❛② ♣r❡❢❡r t♦ ❜✉② ❝r❡❞✐t
r✐s❦ ✐♥ t❤❡ ❜♦♥❞ ♠❛r❦❡t ❜❡❝❛✉s❡ ♦❢ ❛ ❧♦✇❡r ❧✐q✉✐❞✐t② r✐s❦✳ ❍❡♥❝❡✱ ✐♥✈❡st♦rs tr❛❞❡ ❝r❡❞✐t r✐s❦
❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❧✐q✉✐❞✐t② r✐s❦ ✐♥ ❡❛❝❤ ♠❛r❦❡t✳
■♥ ❢✉rt❤❡r r❡s❡❛r❝❤✱ ✇❡ ✐♥t❡♥❞ t♦ ❝♦♥s♦❧✐❞❛t❡ ♦✉r ✜♥❞✐♥❣s ❛♥❞ ❡①t❡♥❞ ♦✉r st✉❞② t♦ ❞❡✈❡❧♦♣❡❞
♠❛r❦❡ts✳ ❙✉❝❤ ❡①t❡♥s✐♦♥ ❝♦✉❧❞ ❜r✐♥❣ ✐♥t♦ ❧✐❣❤t ✈❛❧✉❛❜❧❡ ✐♥❢♦r♠❛t✐♦♥ t♦ ♣♦❧✐❝② ♠❛❦❡rs ❛♥❞
r✐s❦ ♠❛♥❛❣❡rs ♦♥ t❤❡ ❧✐q✉✐❞✐t② ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❞❡✈❡❧♦♣❡❞ ♠❛r❦❡ts ✭❡✳❣✳✱ ❊✉r♦③♦♥❡✮✱ ❡♥❛❜❧❡
✐♥t❡r❡st✐♥❣ ❝♦♠♣❛r❛t✐✈❡ ❛♥❛❧②s✐s ❜❡t✇❡❡♥ ❡♠❡r❣✐♥❣ ❛♥❞ ❞❡✈❡❧♦♣❡❞ ♠❛r❦❡ts ❛♥❞ ♣♦t❡♥t✐❛❧❧②
♣r♦✈✐❞❡ ❢✉rt❤❡r ❡✈✐❞❡♥❝❡ ♦❢ ♥❡❣❛t✐✈❡ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❜♦♥❞ ❛♥❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦✳
✷✹
❘❡❢❡r❡♥❝❡s
❆✉❣✉st✐♥✱ P✳ ✷✵✶✷✳ ✏❚❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❈❉❙ s♣r❡❛❞s ❛♥❞ s♦✈❡r❡✐❣♥ ❝r❡❞✐t r✐s❦✳✑
P❛♣❡r✱ ❙t♦❝❦❤♦❧♠ ❙❝❤♦♦❧ ♦❢ ❊❝♦♥♦♠✐❝s✳
❲♦r❦✐♥❣
❇❛❞❛♦✉✐✱ ❙✳✱ ▲✳ ❈❛t❤❝❛rt✱ ❛♥❞ ▲✳ ❊❧✲❏❛❤❡❧✳ ✷✵✶✸✳ ✏❉♦ s♦✈❡r❡✐❣♥ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣s r❡♣r❡s❡♥t
❛ ❝❧❡❛♥ ♠❡❛s✉r❡ ♦❢ s♦✈❡r❡✐❣♥ ❞❡❢❛✉❧t r✐s❦❄ ❆ ❢❛❝t♦r ♠♦❞❡❧ ❛♣♣r♦❛❝❤✳✑
❛♥❞ ❋✐♥❛♥❝❡ ✸✼✿✷✸✾✷✕✷✹✵✼✳
❇❛✐✱ ❏✳✱ ❈✳ ❏✉❧❧✐❛r❞✱ ❛♥❞ ❑✳ ❨✉❛♥✳
❢✉♥❞❛♠❡♥t❛❧ ❝♦♥t❛❣✐♦♥✳✑
✷✵✶✷✳
❏♦✉r♥❛❧ ♦❢ ❇❛♥❦✐♥❣
✏❊✉r♦③♦♥❡ s♦✈❡r❡✐❣♥ ❜♦♥❞ ❝r✐s✐s✿
❧✐q✉✐❞✐t② ♦r
❲♦r❦✐♥❣ P❛♣❡r✱ ❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❇❛♥❦ ♦❢ ◆❡✇ ❨♦r❦✳
❇❡❜❡r✱ ❆✳ ❇r❛♥❞t✱ ▼ ❲✳✱ ❛♥❞ ❑ ❆✳ ❑❛✈❛❥❡❝③✳ ✷✵✵✾✳ ✏❋❧✐❣❤t✲t♦✲q✉❛❧✐t② ♦r ✢✐❣❤t✲t♦✲❧✐q✉✐❞✐t②❄
❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝✐❛❧ ❙t✉❞✐❡s ✷✷ ✭✸✮✿ ✾✷✺✕✾✺✼✳
✏❉❡❝♦♠♣♦s✐♥❣ ❡✉r♦♣❡❛♥ ❈❉❙ r❡t✉r♥s✳✑ ❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝❡
❊✈✐❞❡♥❝❡ ❢r♦♠ t❤❡ ❡✉r♦✲❛r❡❛ ❜♦♥❞ ♠❛r❦❡t✳✑
❇❡r♥❞t✱ ❆✳✱ ❛♥❞ ■✳ ❖❜r❡❥❛✳ ✷✵✶✵✳
✶✹ ✭✷✮✿ ✶✽✾✕✷✸✸✳
❇♦❧❞❡r✱ ❉✳
✷✵✵✶✳
✏❆✣♥❡ t❡r♠✲str✉❝t✉r❡ ♠♦❞❡❧s✿
P❛♣❡r✱ ❇❛♥❦ ♦❢ ❈❛♥❛❞❛✳
❇♦♥❣❛❡rts✱ ❉✳✱ ❋✳ ❉❡ ❏♦♥❣✱ ❛♥❞ ❏✳ ❉r✐❡ss❡♥✳
❚❤❡♦r② ❛♥❞ ✐♠♣❧❡♠❡♥t❛t✐♦♥✳✑
✷✵✶✶✳
❲♦r❦✐♥❣
✏❉❡r✐✈❛t✐✈❡ ♣r✐❝✐♥❣ ✇✐t❤ ❧✐q✉✐❞✐t② r✐s❦✿
❚❤❡♦r② ❛♥❞ ❡✈✐❞❡♥❝❡ ❢r♦♠ t❤❡ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ ♠❛r❦❡t✳✑
❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝❡ ✻✻
✭✶✮✿ ✷✵✸✕✷✹✵✳
❇✉❤❧❡r✱ ❲✳✱ ❛♥❞ ▼✳ ❚r❛♣♣✳ ✷✵✶✵✳ ✏❚✐♠❡✲✈❛r②✐♥❣ ❝r❡❞✐t r✐s❦ ❛♥❞ ❧✐q✉✐❞✐t② ♣r❡♠✐❛ ✐♥ ❜♦♥❞ ❛♥❞
❈❉❙ ♠❛r❦❡ts✳✑
❲♦r❦✐♥❣ P❛♣❡r✱ ❯♥✐✈❡rs✐t② ♦❢ ❈♦❧♦❣♥❡ ✲ ❈❡♥tr❡ ❢♦r ❋✐♥❛♥❝✐❛❧ ❘❡s❡❛r❝❤✳
❈❛❧✐❝❡✱ ●✳ ❈❤❡♥✱ ❏✳✱ ❛♥❞ ❏ ▼✳ ❲✐❧❧✐❛♠s✳ ✷✵✶✸✳ ✏▲✐q✉✐❞✐t② s♣✐❧❧♦✈❡rs ✐♥ s♦✈❡r❡✐❣♥ ❜♦♥❞ ❛♥❞
❈❉❙ ♠❛r❦❡ts✿ ❆♥ ❛♥❛❧②s✐s ♦❢ t❤❡ ❊✉r♦③♦♥❡ s♦✈❡r❡✐❣♥ ❞❡❜t ❝r✐s✐s✳✑
❇❡❤❛✈✐♦r ❛♥❞ ❖r❣❛♥✐③❛t✐♦♥ ✽✺✿✶✷✷✕✶✹✸✳
❈❤❡♥✱ ❘✳❘✳✱ ❳✳ ❈❤❡♥❣✱ ❋✳❏✳ ❋❛❜♦③③✐✱ ❛♥❞ ❇✳ ▲✐✉✳
✷✵✵✽✳
❞❡❢❛✉❧t s✇❛♣ ♣r✐❝✐♥❣ ♠♦❞❡❧ ✇✐t❤ ❝♦rr❡❧❛t❡❞ ❢❛❝t♦rs✳✑
❆♥❛❧②s✐s ✹✸ ✭✵✶✮✿ ✶✷✸✕✶✻✵✳
❏♦✉r♥❛❧ ♦❢ ❊❝♦♥♦♠✐❝
✏❆♥ ❡①♣❧✐❝✐t✱ ♠✉❧t✐✲❢❛❝t♦r ❝r❡❞✐t
❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝✐❛❧ ❛♥❞ ◗✉❛♥t✐t❛t✐✈❡
❈❤❡♥✱ ❘✳❘✳✱ ❳✳ ❈❤❡♥❣✱ ❛♥❞ ❇✳ ▲✐✉✳ ✷✵✵✽✳ ✏❊st✐♠❛t✐♦♥ ❛♥❞ ❡✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ t❡r♠ str✉❝t✉r❡
♦❢ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣s✿ ❆♥ ❡♠♣✐r✐❝❛❧ st✉❞②✳✑
■♥s✉r❛♥❝❡✿ ▼❛t❤❡♠❛t✐❝s ❛♥❞ ❊❝♦♥♦♠✐❝s ✹✸
✭✸✮✿ ✸✸✾✕✸✹✾✳
❈❤❡♥✱ ❘✳❘✳✱ ❳✳ ❈❤❡♥❣✱ ❛♥❞ ▲✳ ❲✉✳ ✷✵✶✶✳ ✏❉②♥❛♠✐❝ ✐♥t❡r❛❝t✐♦♥s ❜❡t✇❡❡♥ ✐♥t❡r❡st r❛t❡✱ ❝r❡❞✐t✱
❛♥❞ ❧✐q✉✐❞✐t② r✐s❦s✿ ❚❤❡♦r② ❛♥❞ ❡✈✐❞❡♥❝❡ ❢r♦♠ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣
s♣r❡❛❞s✳✑
❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝❡✱ ✈♦❧✳ ✼✼✾✹✹✺✳
❈❤❡♥✱ ❘✳❘✳✱ ❋✳❏✳ ❋❛❜♦③③✐✱ ❛♥❞ ❘✳ ❙✈❡r❞❧♦✈❡✳ ✷✵✶✵✳ ✏❈♦r♣♦r❛t❡ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ ❧✐q✉✐❞✐t②
❛♥❞ ✐ts ✐♠♣❧✐❝❛t✐♦♥s ❢♦r ❝♦r♣♦r❛t❡ ❜♦♥❞ s♣r❡❛❞s✳✑
❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❋✐①❡❞ ■♥❝♦♠❡
✷✵ ✭✷✮✿
✸✶✕✺✼✳
❈❤❡♥✱ ❘✳❘✳✱ ❛♥❞ ▲✳ ❙❝♦tt✳ ✷✵✵✸✳ ✏▼✉❧t✐✲❢❛❝t♦r ❈♦①✲■♥❣❡rs♦❧❧✲❘♦ss ♠♦❞❡❧s ♦❢ t❤❡ t❡r♠ str✉❝✲
t✉r❡✿
❊st✐♠❛t❡s ❛♥❞ t❡sts ❢r♦♠ ❛ ❑❛❧♠❛♥ ✜❧t❡r ♠♦❞❡❧✳✑
❋✐♥❛♥❝❡ ❛♥❞ ❊❝♦♥♦♠✐❝s ✷✼ ✭✷✮✿ ✶✹✸✕✶✼✷✳
❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❘❡❛❧ ❊st❛t❡
❉❡ ❏♦♥❣✱ ❋✳ ✷✵✵✵✳ ✏❚✐♠❡ s❡r✐❡s ❛♥❞ ❝r♦ss✲s❡❝t✐♦♥ ✐♥❢♦r♠❛t✐♦♥ ✐♥ ❛✣♥❡ t❡r♠✲str✉❝t✉r❡ ♠♦❞❡❧s✳✑
❏♦✉r♥❛❧ ♦❢ ❇✉s✐♥❡ss ✫ ❊❝♦♥♦♠✐❝ ❙t❛t✐st✐❝s✱ ♣♣✳ ✸✵✵✕✸✶✹✳
✷✺
❊❥s✐♥❣✱ ❏✳ ●r♦t❤❡✱ ▼✳✱ ❛♥❞ ❖✳ ●r♦t❤❡✳ ✷✵✶✷✳ ✏▲✐q✉✐❞✐t② ❛♥❞ ❝r❡❞✐t r✐s❦ ♣r❡♠✐❛ ✐♥ ❣♦✈❡r♥♠❡♥t
❜♦♥❞ ②✐❡❧❞s✳✑ ❲♦r❦✐♥❣ P❛♣❡r✱ ❊✉r♦♣❡❛♥ ❈❡♥tr❛❧ ❇❛♥❦✳
●♦②❡♥❦♦✱ ❘✳✱ ❆✳ ❙✉❜r❛❤♠❛♥②❛♠✱ ❛♥❞ ❆✳ ❯❦❤♦✈✳ ✷✵✶✶✳ ✏❚❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❜♦♥❞ ♠❛r✲
❦❡t ❧✐q✉✐❞✐t② ❛♥❞ ✐ts ✐♠♣❧✐❝❛t✐♦♥s ❢♦r ❡①♣❡❝t❡❞ ❜♦♥❞ r❡t✉r♥s✳✑
❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝✐❛❧ ❛♥❞
◗✉❛♥t✐t❛t✐✈❡ ❆♥❛❧②s✐s ✹✻ ✭✶✮✿ ✶✶✶✳
❍❛♥✱ ❇✳✱ ❛♥❞ ❨✳ ❩❤♦✉✳
✷✵✶✶✳
✏❚❡r♠ str✉❝t✉r❡ ♦❢ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ s♣r❡❛❞s ❛♥❞ ❝r♦ss✲
s❡❝t✐♦♥ ♦❢ st♦❝❦ r❡t✉r♥s✳✑ ❲♦r❦✐♥❣ P❛♣❡r✱ ❯♥✐✈❡rs✐t② ♦❢ ❚❡①❛s ❛t ❆✉st✐♥ ❛♥❞ ❋❧♦r✐❞❛ ❙t❛t❡
❯♥✐✈❡rs✐t②✱ ❉❡♣❛rt♠❡♥t ♦❢ ❋✐♥❛♥❝❡✳
❏❛rr♦✇✱ ❘✳✱ ❍✳ ▲✐✱ ❛♥❞ ❳✳ ❨❡✳ ✷✵✵✾✳ ✏❊①♣❧♦r✐♥❣ st❛t✐st✐❝❛❧ ❛r❜✐tr❛❣❡ ♦♣♣♦rt✉♥✐t✐❡s ✐♥ t❤❡ t❡r♠
str✉❝t✉r❡ ♦❢ ❈❉❙ s♣r❡❛❞s✳✑
❲♦r❦✐♥❣ P❛♣❡r✱ ❏♦❤♥s♦♥ ●r❛❞✉❛t❡ ❙❝❤♦♦❧ ♦❢ ▼❛♥❛❣❡♠❡♥t✱
❈♦r♥❡❧❧ ❯♥✐✈❡rs✐t②✳
❑❡♠♣❢✱ ❆✳ ❑♦r♥✱ ❖✳✱ ❛♥❞ ▼✳ ❯❤r✐❣✲❍♦♠❜✉r❣✳ ✷✵✶✷✳ ✏❚❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ✐❧❧✐q✉✐❞✐t② ♣r❡♠✐❛✳✑
❏♦✉r♥❛❧ ♦❢ ❇❛♥❦✐♥❣ ❛♥❞ ❋✐♥❛♥❝❡ ✸✻ ✭✺✮✿ ✶✸✽✶✕✶✸✾✶✳
▲✐♥✱ ❍✳✱ ❙✳ ▲✐✉✱ ❛♥❞ ❈✳ ❲✉✳ ✷✵✵✾✳ ✏▲✐q✉✐❞✐t② ♣r❡♠✐❛ ✐♥ t❤❡ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ ❛♥❞ ❝♦r♣♦✲
r❛t❡ ❜♦♥❞ ♠❛r❦❡ts✳✑
❲♦r❦✐♥❣ P❛♣❡r✱ ❯♥✐✈❡rs✐t② ♦❢ ❖t❛❣♦ ✲ ❉❡♣❛rt♠❡♥t ♦❢ ❋✐♥❛♥❝❡ ❛♥❞
◗✉❛♥t✐t❛t✐✈❡ ❆♥❛❧②s✐s✳
▲♦♥❣st❛✛✱ ❋✳ ❆✳ ✷✵✵✹✳ ✏❚❤❡ ✢✐❣❤t✲t♦✲❧✐q✉✐❞✐t② ♣r❡♠✐✉♠ ✐♥ ❯✳❙✳ tr❡❛s✉r② ❜♦♥❞ ♣r✐❝❡s✳✑ ❏♦✉r♥❛❧
♦❢ ❇✉s✐♥❡ss ✼✼✿✺✶✶✕✺✷✻✳
▲♦♥❣st❛✛✱ ❋✳❆✳✱ ❙✳ ▼✐t❤❛❧✱ ❛♥❞ ❊✳ ◆❡✐s✳
✷✵✵✺✳
✏❈♦r♣♦r❛t❡ ②✐❡❧❞ s♣r❡❛❞s✿ ❉❡❢❛✉❧t r✐s❦ ♦r
❧✐q✉✐❞✐t②❄ ◆❡✇ ❡✈✐❞❡♥❝❡ ❢r♦♠ t❤❡ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ ♠❛r❦❡t✳✑ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝❡
✻✵ ✭✺✮✿ ✷✷✶✸✕✷✷✺✸✳
▲♦♥❣st❛✛✱ ❋✳❆✳✱ ❏✳ P❛♥✱ ▲✳❍✳ P❡❞❡rs❡♥✱ ❛♥❞ ❑✳❏✳ ❙✐♥❣❧❡t♦♥✳ ✷✵✶✶✳ ✏❍♦✇ s♦✈❡r❡✐❣♥ ✐s s♦✈❡r❡✐❣♥
❝r❡❞✐t r✐s❦❄✑ ❆♠❡r✐❝❛♥ ❊❝♦♥♦♠✐❝ ❏♦✉r♥❛❧✿ ▼❛❝r♦❡❝♦♥♦♠✐❝s✱ ♥♦✳ ✸✿✼✺✕✶✵✸✳
▼♦♥❢♦rt✱ ❆✳✱ ❛♥❞ P✳ ❘❡♥♥❡✳
✷✵✶✶✳
✏❈r❡❞✐t ❛♥❞ ❧✐q✉✐❞✐t② r✐s❦s ✐♥ ❡✉r♦✲❛r❡❛ s♦✈❡r❡✐❣♥ ②✐❡❧❞
❝✉r✈❡s✳✑ ❲♦r❦✐♥❣ P❛♣❡r✱ ❇❛♥q✉❡ ❞❡ ❋r❛♥❝❡✳
P❛♥✱ ❏✳✱ ❛♥❞ ❑✳❏✳ ❙✐♥❣❧❡t♦♥✳ ✷✵✵✽✳ ✏❉❡❢❛✉❧t ❛♥❞ r❡❝♦✈❡r② ✐♠♣❧✐❝✐t ✐♥ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢
s♦✈❡r❡✐❣♥ ❈❉❙ s♣r❡❛❞s✳✑ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝❡ ✻✸ ✭✺✮✿ ✷✸✹✺✕✷✸✽✹✳
P❡❧✐③③♦♥✱ ▲✳✱ ▼✳ ●✳ ❙✉❜r❛❤♠❛♥②❛♠✱ ❉✳ ❚♦♠✐♦✱ ❛♥❞ ❏✳ ❯♥♦✳ ✷✵✶✸✳ ✏❚❤❡ ▼✐❝r♦str✉❝t✉r❡ ♦❢
t❤❡ ❊✉r♦♣❡❛♥ ❙♦✈❡r❡✐❣♥ ❇♦♥❞ ▼❛r❦❡t✿ ❆ ❙t✉❞② ♦❢ t❤❡ ❊✉r♦✲③♦♥❡ ❈r✐s✐s✳✑ ❲♦r❦✐♥❣ P❛♣❡r✱
❙t❡r♥ ❙❝❤♦♦❧ ♦❢ ❇✉s✐♥❡ss✳
◗✐✉✱ ❏✳✱ ❛♥❞ ❋✳ ❨✉✳ ✷✵✶✷✳ ✏❊♥❞♦❣❡♥♦✉s ❧✐q✉✐❞✐t② ✐♥ ❝r❡❞✐t ❞❡r✐✈❛t✐✈❡s✳✑ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝✐❛❧
❊❝♦♥♦♠✐❝s ✶✵✸✿✻✶✶✕✻✸✶✳
❙❝❤✉st❡r✱ P✳✱ ▼✳ ❚r❛♣♣✱ ❛♥❞ ▼✳ ❯❤r✐❣✲❍♦♠❜✉r❣✳
✷✵✶✸✳
✏❆ ❤❡t❡r♦❣❡♥❡♦✉s ❛❣❡♥ts ❡q✉✐❧✐❜✲
r✐✉♠ ♠♦❞❡❧ ❢♦r t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❜♦♥❞ ♠❛r❦❡t ❧✐q✉✐❞✐t②✳✑ ❲♦r❦✐♥❣ P❛♣❡r✱ ❑❛r❧sr✉❤❡
■♥st✐t✉t❡ ♦❢ ❚❡❝❤♥♦❧♦❣②✳
❙❝❤✉st❡r✱ P✳✱ ❛♥❞ ▼✳ ❯❤r✐❣✲❍♦♠❜✉r❣✳ ✷✵✶✷✳ ✏❚❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❜♦♥❞ ♠❛r❦❡t ❧✐q✉✐❞✐t②
❝♦♥❞✐t✐♦♥❛❧ ♦♥ t❤❡ ❡❝♦♥♦♠✐❝ ❡♥✈✐r♦♥♠❡♥t✿ ❆♥ ❛♥❛❧②s✐s ♦❢ ❣♦✈❡r♥♠❡♥t ❣✉❛r❛♥t❡❡❞ ❜♦♥❞s✳✑
❲♦r❦✐♥❣ P❛♣❡r✱ ❑❛r❧sr✉❤❡ ■♥st✐t✉t❡ ♦❢ ❚❡❝❤♥♦❧♦❣②✳
✷✻
❚❛♥❣✱ ❉✳❨✳✱ ❛♥❞ ❍✳ ❨❛♥✳ ✷✵✵✼✳ ✏▲✐q✉✐❞✐t② ❛♥❞ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣ s♣r❡❛❞s✳✑ ❲♦r❦✐♥❣ P❛♣❡r✱
❯♥✐✈❡rs✐t② ♦❢ ❍♦♥❣ ❑♦♥❣ ✲ ❙❝❤♦♦❧ ♦❢ ❊❝♦♥♦♠✐❝s ❛♥❞ ❋✐♥❛♥❝❡✳
❚r✉❝❦✱ ❙✳✱ ▼✳ ▲❛✉❜✱ ❛♥❞ ❙✳❚✳ ❘❛❝❤❡✈✳
✷✵✵✹✳
✏❚❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❝r❡❞✐t s♣r❡❛❞s ❛♥❞
❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣s✲❛♥ ❡♠♣✐r✐❝❛❧ ✐♥✈❡st✐❣❛t✐♦♥✳✑ ❏♦✉r♥❛❧ ♦❢ ■♥✈❡st♠❡♥t ▼❛♥❛❣❡♠❡♥t ❛♥❞
❋✐♥❛♥❝✐❛❧ ■♥♥♦✈❛t✐♦♥s✱ ✈♦❧✳ ✸✳
❲❤✐t❡✱ ❍✳ ✶✾✽✷✳ ✏❘❡❣✉❧❛r✐t② ❝♦♥❞✐t✐♦♥s ❢♦r ❈♦①✬s t❡st ♦❢ ♥♦♥✲♥❡st❡❞ ❤②♣♦t❤❡s❡s✳✑ ❏♦✉r♥❛❧ ♦❢
❊❝♦♥♦♠❡tr✐❝s ✶✾ ✭✷✮✿ ✸✵✶✕✸✶✽✳
❩❤❛♥❣✱ ❋✳❳✳
✷✵✵✽✳
✏▼❛r❦❡t ❡①♣❡❝t❛t✐♦♥s ❛♥❞ ❞❡❢❛✉❧t r✐s❦ ♣r❡♠✐✉♠ ✐♥ ❝r❡❞✐t ❞❡❢❛✉❧t s✇❛♣
♣r✐❝❡s✳✑ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❋✐①❡❞ ■♥❝♦♠❡ ✶✽ ✭✶✮✿ ✸✼✕✺✺✳
✷✼
❋✐❣✉r❡s
❋✐❣✉r❡ ✶✿
❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ ❚❡r♠ ❙tr✉❝t✉r❡ ❇r❛③✐❧
❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ ❡st✐♠❛t❡❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✭✐♥ ❞❡❝✐♠❛❧s✮ ♦❢ t❤❡ ✶✱ ✸✱ ✺✱ ✼
❛♥❞ ✶✵ ②❡❛r ♠❛t✉r✐t② ❢♦r ❇r❛③✐❧✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ y CDS ❜② ✉s✐♥❣ t❤❡ ❞✐s❝r❡t❡✲t✐♠❡
❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ♠✐❞ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ y CDS
✐s ❡q✉❛❧ t♦ zCDS ✇❤✐❝❤ ✐s ♦✉r ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❢♦r ❇r❛③✐❧✳
✷✽
❋✐❣✉r❡ ✷✿
❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ ❚❡r♠ ❙tr✉❝t✉r❡ P❤✐❧✐♣♣✐♥❡s
❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ ❡st✐♠❛t❡❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✭✐♥ ❞❡❝✐♠❛❧s✮ ♦❢ t❤❡ ✶✱ ✸✱ ✺✱ ✼
❛♥❞ ✶✵ ②❡❛r ♠❛t✉r✐t② ❢♦r P❤✐❧✐♣♣✐♥❡s✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ y CDS ❜② ✉s✐♥❣ t❤❡ ❞✐s❝r❡t❡✲
t✐♠❡ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ♠✐❞ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳
y CDS ✐s ❡q✉❛❧ t♦ zCDS ✇❤✐❝❤ ✐s ♦✉r ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❢♦r P❤✐❧✐♣♣✐♥❡s✳
✷✾
❋✐❣✉r❡ ✸✿
❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ ❚❡r♠ ❙tr✉❝t✉r❡ ❚✉r❦❡②
❚❤✐s ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ ❡st✐♠❛t❡❞ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ✭✐♥ ❞❡❝✐♠❛❧s✮ ♦❢ t❤❡ ✶✱ ✸✱ ✺✱ ✼
❛♥❞ ✶✵ ②❡❛r ♠❛t✉r✐t② ❢♦r ❚✉r❦❡②✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ y CDS ❜② ✉s✐♥❣ t❤❡ ❞✐s❝r❡t❡✲t✐♠❡
❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ♠✐❞ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ y CDS
✐s ❡q✉❛❧ t♦ zCDS ✇❤✐❝❤ ✐s ♦✉r ✉♣♣❡r ❜♦✉♥❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❢♦r ❚✉r❦❡②✳
✸✵
❋✐❣✉r❡ ✹✿
❇♦♥❞ ❛♥❞ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ ❚❡r♠ ❙tr✉❝t✉r❡✿ ❇r❛③✐❧
❚❤❡ ✭t♦♣✮ ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ ❡st✐♠❛t❡❞ ❤❛③❛r❞ r❛t❡ ✭♦r ❞❡❢❛✉❧t ✐♥t❡♥s✐t②✮ ♦❢ t❤❡
✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛r ♠❛t✉r✐t② ❢♦r ❇r❛③✐❧✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❤❛③❛r❞ r❛t❡ h ❜② ✉s✐♥❣ ❛ ❞✐s❝r❡t❡✲t✐♠❡
❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ❛s❦ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ ❚❤❡
✮ ❢♦r
✭❜♦tt♦♠✮ ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ r❛t✐♦ ♦❢ ❈❉❙ ♦✈❡r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✭✐✳❡✳ zzCDS
bond
CDS
❇r❛③✐❧✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ zCDS ✭❂ y
✮ ❜② ✉s✐♥❣ t❤❡ ❞✐s❝r❡t❡✲t✐♠❡ ❛♣♣r♦①✐♠❛t✐♦♥
♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ♠✐❞ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ ■♥ ♦r❞❡r t♦ ❡st✐♠❛t❡
❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✱ ✇❡ ✜rst ♥❡❡❞ t♦ ♠❛t❝❤ ❜♦♥❞ ♠❛t✉r✐t✐❡s ✇✐t❤ ❈❉❙ ♠❛t✉r✐t✐❡s✳ ❚♦ ♣r♦①② ❢♦r t❤❡ ✶
②❡❛r ♠❛t✉r✐t② ❜♦♥❞✱ ✇❡ ✉s❡ t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❡ ❤❛✈❡ ❢♦r ❇r❛③✐❧ ✇❤✐❝❤ ✐s ✵✽✴✷✵✶✶✳ ❚♦ ♣r♦①②
t❤❡ ✸ ②❡❛rs ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ✉s❡ ❜♦♥❞s t❤❛t ❡①♣✐r❡ r✐❣❤t ❛❢t❡r t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❤✐❝❤
✐s ✵✶✴✷✵✶✷✳ ❋♦r t❤❡ ✺ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝❤♦♦s❡ ❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❞♦ ♥♦t ❡①❝❡❡❞
✷✵✶✺ ✭✐✳❡✳ ✵✸✴✷✵✶✺✮✳ ❋♦r t❤❡ ✼ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ♣✐❝❦ ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❛r❡
❛r♦✉♥❞ ✷✵✶✼ ✭✐✳❡✳ ✵✶✴✷✵✶✽✮✳ ❋✐♥❛❧❧② t♦ ♣r♦①② ❢♦r t❤❡ ✶✵ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝♦❧❧❡❝t ❜♦♥❞s t❤❛t
❤❛✈❡ ♠❛t✉r✐t✐❡s t❤❛t ❛r❡ ❛s ❝❧♦s❡ ❛s ♣♦ss✐❜❧❡ t♦ ✷✵✷✵ ✭✐✳❡✳ ✵✶✴✷✵✷✵✮✳ ❖✉r ❞❛t❛ s❡t r✉♥s ❢r♦♠ ✵✶✴✶✶✴✷✵✵✺
t♦ ✸✵✴✵✾✴✷✵✶✵✳ ❖♥❝❡ ✇❡ ♠❛t❝❤ ❛s ❝❧♦s❡❧② ❛s ♣♦ss✐❜❧❡ ❈❉❙ ♠❛t✉r✐t✐❡s✱ ✇❡ ❡st✐♠❛t❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦
zbond ❜② t❛❦✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♠✐❞ ❛♥❞ t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ❛s❦✳
✸✶
❋✐❣✉r❡ ✺✿
❇♦♥❞ ❛♥❞ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ ❚❡r♠ ❙tr✉❝t✉r❡✿ P❤✐❧✐♣♣✐♥❡s
❚❤❡ ✭t♦♣✮ ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ ❡st✐♠❛t❡❞ ❤❛③❛r❞ r❛t❡ ✭♦r ❞❡❢❛✉❧t ✐♥t❡♥s✐t②✮ ♦❢ t❤❡ ✶✱
✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛r ♠❛t✉r✐t② ❢♦r P❤✐❧✐♣♣✐♥❡s✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❤❛③❛r❞ r❛t❡ h ❜② ✉s✐♥❣ ❛ ❞✐s❝r❡t❡✲t✐♠❡
❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ❛s❦ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ ❚❤❡
✭❜♦tt♦♠✮ ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ r❛t✐♦ ♦❢ ❈❉❙ ♦✈❡r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✭✐✳❡✳ zzCDS
bond
✮ ❢♦r P❤✐❧✐♣♣✐♥❡s✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ zCDS ✭❂y CDS ✮ ❜② ✉s✐♥❣ t❤❡ ❞✐s❝r❡t❡✲t✐♠❡
❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ♠✐❞ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ ■♥
♦r❞❡r t♦ ❡st✐♠❛t❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✱ ✇❡ ✜rst ♥❡❡❞ t♦ ♠❛t❝❤ ❜♦♥❞ ♠❛t✉r✐t✐❡s ✇✐t❤ ❈❉❙ ♠❛t✉r✐t✐❡s✳ ❚♦
♣r♦①② ❢♦r t❤❡ ✶ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞✱ ✇❡ ✉s❡ t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❡ ❤❛✈❡ ✇❤✐❝❤ ✐s ✵✷✴✷✵✶✸ ❢♦r
P❤✐❧✐♣♣✐♥❡s✳ ❚♦ ♣r♦①② t❤❡ ✸ ②❡❛rs ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ✉s❡ ❜♦♥❞s t❤❛t ❡①♣✐r❡ r✐❣❤t ❛❢t❡r t❤❡ s❤♦rt❡st
♠❛t✉r✐t② ❜♦♥❞ ✭✐✳❡✳ ✵✶✴✷✵✶✹✮✳ ❋♦r t❤❡ ✺ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝❤♦♦s❡ ❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t② ❞❛t❡s
t❤❛t ❞♦ ♥♦t ❡①❝❡❡❞ ✷✵✶✺ ✭✐✳❡✳ ✵✸✴✷✵✶✺✮✳ ❋♦r t❤❡ ✼ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ♣✐❝❦ ❜♦♥❞s t❤❛t ❤❛✈❡
♠❛t✉r✐t② ❞❛t❡s t❤❛t ❛r❡ ❛r♦✉♥❞ ✷✵✶✼ ✭✐✳❡✳ ✵✶✴✷✵✶✼✮✳ ❋✐♥❛❧❧② t♦ ♣r♦①② ❢♦r t❤❡ ✶✵ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱
✇❡ ❝♦❧❧❡❝t ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t✐❡s t❤❛t ❛r❡ ❛s ❝❧♦s❡ ❛s ♣♦ss✐❜❧❡ t♦ ✷✵✷✵ ✭✐✳❡✳ ✶✵✴✷✵✷✹✮✳ ❖✉r ❞❛t❛
s❡t r✉♥s ❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✵✴✵✾✴✷✵✶✵✳ ❖♥❝❡ ✇❡ ♠❛t❝❤ ❛s ❝❧♦s❡❧② ❛s ♣♦ss✐❜❧❡ ❈❉❙ ♠❛t✉r✐t✐❡s✱ ✇❡
❡st✐♠❛t❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ zbond ❜② t❛❦✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♠✐❞ ❛♥❞ t❤❡
②✐❡❧❞✲t♦✲♠❛t✉r✐t② ❛s❦✳
✸✷
❋✐❣✉r❡ ✻✿
❇♦♥❞ ❛♥❞ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦ ❚❡r♠ ❙tr✉❝t✉r❡✿ ❚✉r❦❡②
❚❤❡ ✭t♦♣✮ ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ ❡st✐♠❛t❡❞ ❤❛③❛r❞ r❛t❡ ✭♦r ❞❡❢❛✉❧t ✐♥t❡♥s✐t②✮ ♦❢ t❤❡
✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛r ♠❛t✉r✐t② ❢♦r ❚✉r❦❡②✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❤❛③❛r❞ r❛t❡ h ❜② ✉s✐♥❣ ❛ ❞✐s❝r❡t❡✲t✐♠❡
❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ❛s❦ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ ❚❤❡
✮ ❢♦r
✭❜♦tt♦♠✮ ✜❣✉r❡ s❤♦✇s t❤❡ t✐♠❡ s❡r✐❡s ♣❧♦t ♦❢ t❤❡ r❛t✐♦ ♦❢ ❈❉❙ ♦✈❡r ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ✭✐✳❡✳ zzCDS
bond
CDS
❚✉r❦❡②✳ ❲❡ ❡st✐♠❛t❡ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ zCDS ✭❂y
✮ ❜② ✉s✐♥❣ t❤❡ ❞✐s❝r❡t❡✲t✐♠❡ ❛♣♣r♦①✐♠❛t✐♦♥
♦❢ t❤❡ ❈❉❙ ♣r✐❝✐♥❣ ❢♦r♠✉❧❛ r❡❧❛t❡❞ t♦ t❤❡ ♠✐❞ q✉♦t❡ ❛♥❞ ❞❡✜♥❡❞ ✐♥ ❙❡❝t✐♦♥ ✺✳✶✳ ■♥ ♦r❞❡r t♦ ❡st✐♠❛t❡
❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦✱ ✇❡ ✜rst ♥❡❡❞ t♦ ♠❛t❝❤ ❜♦♥❞ ♠❛t✉r✐t✐❡s ✇✐t❤ ❈❉❙ ♠❛t✉r✐t✐❡s✳ ❚♦ ♣r♦①② ❢♦r t❤❡
✶ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞✱ ✇❡ ✉s❡ t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❡ ❤❛✈❡ ✇❤✐❝❤ ✐s ✵✻✴✷✵✶✶✳ ❚♦ ♣r♦①② t❤❡ ✸
②❡❛rs ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ✉s❡ ❜♦♥❞s t❤❛t ❡①♣✐r❡ r✐❣❤t ❛❢t❡r t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✭✐✳❡✳ ✵✶✴✷✵✶✸✮✳
❋♦r t❤❡ ✺ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝❤♦♦s❡ ❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❞♦ ♥♦t ❡①❝❡❡❞ ✷✵✶✺ ✭✐✳❡✳
✵✸✴✷✵✶✺✮✳ ❋♦r t❤❡ ✼ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ♣✐❝❦ ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❛r❡ ❛r♦✉♥❞ ✷✵✶✼
✭✐✳❡✳ ✵✼✴✷✵✶✼✮✳ ❋✐♥❛❧❧② t♦ ♣r♦①② ❢♦r t❤❡ ✶✵ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝♦❧❧❡❝t ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t✐❡s
t❤❛t ❛r❡ ❛s ❝❧♦s❡ ❛s ♣♦ss✐❜❧❡ t♦ ✷✵✷✵ ✭✐✳❡✳ ✵✷✴✷✵✷✺ ❚✉r❦❡②✮✳ ❖✉r ❞❛t❛ s❡t r✉♥s ❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦
✸✵✴✵✾✴✷✵✶✵✳ ❖♥❝❡ ✇❡ ♠❛t❝❤ ❛s ❝❧♦s❡❧② ❛s ♣♦ss✐❜❧❡ ❈❉❙ ♠❛t✉r✐t✐❡s✱ ✇❡ ❡st✐♠❛t❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦
zbond ❜② t❛❦✐♥❣ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ♠✐❞ ❛♥❞ t❤❡ ②✐❡❧❞✲t♦✲♠❛t✉r✐t② ❛s❦✳
✸✸
❋✐❣✉r❡ ✼✿
❇♦♥❞ ❛♥❞ ❈❉❙ ❚✐♠❡ ❱❛r②✐♥❣ ▲✐q✉✐❞✐t② ❘✐s❦ Pr❡♠✐✉♠✿ Pr❡✲❈r✐s✐s ❚✐♠❡
❚❤❡ ✜❣✉r❡ s❤♦✇s t❤❡ ♣❧♦t ♦❢ t❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✭∆(y CDS (t) ∗ λ1 )
❛♥❞ ∆(y bond (t) ∗ λ2 )✮ ❡①tr❛❝t❡❞ ❢r♦♠ t❤❡ ❑❛❧♠❛♥ ✜❧t❡r ❡st✐♠❛t✐♦♥ ✇❤❡r❡ y CDS (t) ❛♥❞ y bond (t)✮ ❛r❡ t❤❡
st❛t❡ ✈❛r✐❛❜❧❡s ♦❢ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ r❡s♣❡❝t✐✈❡❧② ❛♥❞ λ1 ❛♥❞ λ2 ❛r❡ t❤❡ ♠❛r❦❡t ♣r✐❝❡s ♦❢
r✐s❦ ♦❢ ❜♦t❤ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠ ❛r❡ s❤♦✇♥ ❢♦r ❛❧❧ ❝♦✉♥tr✐❡s ✭✐✳❡✳ ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✮ ❛♥❞ ❢♦r t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞
✭❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽✮✳
✸✹
❋✐❣✉r❡ ✽✿
❇♦♥❞ ❛♥❞ ❈❉❙ ❚✐♠❡ ❱❛r②✐♥❣ ▲✐q✉✐❞✐t② ❘✐s❦ Pr❡♠✐✉♠✿ ❈r✐s✐s ❚✐♠❡
❚❤❡ ✜❣✉r❡ s❤♦✇s t❤❡ ♣❧♦t ♦❢ t❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✭∆(y CDS (t) ∗ λ1 )
❛♥❞ ∆(y bond (t) ∗ λ2 )✮ ❡①tr❛❝t❡❞ ❢r♦♠ t❤❡ ❑❛❧♠❛♥ ✜❧t❡r ❡st✐♠❛t✐♦♥ ✇❤❡r❡ y CDS (t) ❛♥❞ y bond (t)✮ ❛r❡ t❤❡
st❛t❡ ✈❛r✐❛❜❧❡s ♦❢ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ r❡s♣❡❝t✐✈❡❧② ❛♥❞ λ1 ❛♥❞ λ2 ❛r❡ t❤❡ ♠❛r❦❡t ♣r✐❝❡s ♦❢
r✐s❦ ♦❢ ❜♦t❤ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦
♣r❡♠✐✉♠ ❛r❡ ♣r❡s❡♥t❡❞ ❢♦r ❛❧❧ ❝♦✉♥tr✐❡s ✭✐✳❡✳ ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✮ ❛♥❞ ❢♦r t❤❡ ❝r✐s✐s ♣❡r✐♦❞
✭❢r♦♠ ✵✶✴✵✹✴✷✵✵✽ t♦ ✸✵✴✵✾✴✷✵✶✵✮✳
✸✺
❚❛❜❧❡ ✶✿
❉❡s❝r✐♣t✐♦♥ ♦❢ ❇♦♥❞ ❉❛t❛ ❢♦r ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②
✭❆▼❨✮✱ ♠❛t✉r✐t② ❞❛t❡s✱ ❝♦✉♣♦♥ ♣❛②♠❡♥t r❛t❡s ❛♥❞ ✐ss✉❡ ❞❛t❡s✳ ❲❡ s❤♦✇ t❤❡ ❛✈❡r❛❣❡ ♠✐❞ ②✐❡❧❞ ♦✈❡r t❤❡ ❡♥t✐r❡ s❛♠♣❧❡ ♣❡r✐♦❞ ✭❢r♦♠
◆♦✈❡♠❜❡r ✷✵✵✺ t♦ ❙❡♣t❡♠❜❡r ✷✵✶✵✮✳
❇r❛③✐❧
▼❛t✉r✐t② ✵✽✴✷✵✶✶ ✵✶✴✷✵✶✷ ✵✻✴✷✵✶✸ ✵✼✴✷✵✶✹ ✵✸✴✷✵✶✺ ✵✶✴✷✵✶✼ ✵✶✴✷✵✶✽ ✵✶✴✷✵✶✾ ✶✵✴✷✵✶✾ ✵✶✴✷✵✷✵ ✵✹✴✷✵✷✹ ✵✹✴✷✵✷✹
❈♦✉♣♦♥
✶✵✪
✶✶✪
✹✪
✷✪
✽✪
✻✪
✽✪
✽✪
✽✪
✹✪
✽✪
✽✪
❆▼❨
✵✳✵✸✼
✵✳✵✹✶
✵✳✵✹✷ ✵✳✵✺✶✹ ✵✳✵✺✸✹ ✵✳✵✺✶
✵✳✵✻✷
✵✳✵✹✼ ✵✳✵✻✵✹ ✵✳✵✻✶
✵✳✵✻✹
✵✳✵✻✹
■ss✉❡ ❉❛t❡ ✷✵✵✸
✷✵✵✷
✷✵✵✸
✷✵✵✹
✷✵✵✺
✷✵✵✻
✷✵✵✺
✷✵✵✾
✷✵✵✹
✷✵✵✵
✷✵✵✸
✷✵✵✶
▼❛t✉r✐t② ✵✷✴✷✵✷✺ ✵✸✴✷✵✸✵ ✵✶✴✷✵✸✹ ✵✶✴✷✵✸✼ ✵✽✴✷✵✹✵ ✵✶✴✷✵✹✶
❈♦✉♣♦♥
✹✪
✹✪
✹✪
✽✪
✶✶✪
✽✪
❆▼❨
✵✳✵✻✹✹ ✵✳✵✻✻✾ ✵✳✵✻✻✹ ✵✳✵✻✹ ✵✳✵✽✷✽ ✵✳✵✺✻✷
■ss✉❡ ❉❛t❡ ✷✵✵✺
✷✵✵✵
✷✵✵✹
✷✵✵✻
✷✵✵✵
✷✵✵✾
P❤✐❧✐♣♣✐♥❡s
✸✻
▼❛t✉r✐t② ✵✷✴✷✵✶✸ ✵✶✴✷✵✶✹ ✵✸✴✷✵✶✺ ✵✶✴✷✵✶✻ ✶✵✴✷✵✶✻ ✵✶✴✷✵✶✼ ✵✶✴✷✵✶✾ ✵✻✴✷✵✶✾ ✵✶✴✷✵✷✵ ✶✵✴✷✵✷✹ ✵✾✴✷✵✷✹ ✵✸✴✷✵✷✺
❈♦✉♣♦♥
✾✪
✹✪
✽✪
✽✪
✹✪
✽✪
✽✪
✽✪
✷✪
✷✪
✷✪
✽✪
❆▼❨
✵✳✵✺✶✾ ✵✳✵✺✹✼ ✵✳✵✺✻✵ ✵✳✵✹✺
✵✳✵✻
✵✳✵✻✵✼ ✵✳✵✻✹ ✵✳✵✼✷✹ ✵✳✵✹✽
✵✳✵✻✽
✵✳✵✻✹
✵✳✵✻✾
■ss✉❡ ❉❛t❡ ✷✵✵✷
✷✵✵✸
✷✵✵✹
✷✵✵✺
✶✾✾✻
✷✵✵✷
✶✾✾✾
✷✵✵✾
✷✵✵✾
✶✾✾✾
✷✵✵✻
✷✵✵✵
▼❛t✉r✐t② ✵✷✴✷✵✸✵ ✵✶✴✷✵✸✶ ✵✶✴✷✵✸✷
❈♦✉♣♦♥
✷✪
✹✪
✽✪
❆▼❨
✵✳✵✼
✵✳✵✻✽
✵✳✵✻✺
■ss✉❡ ❉❛t❡ ✷✵✵✺
✷✵✵✻
✷✵✵✼
❚✉r❦❡②
▼❛t✉r✐t② ✵✻✴✷✵✶✶ ✵✶✴✷✵✶✷ ✵✶✴✷✵✶✸ ✵✶✴✷✵✶✹ ✵✸✴✷✵✶✺ ✵✾✴✷✵✶✻ ✵✼✴✷✵✶✼ ✵✹✴✷✵✶✽ ✵✸✴✷✵✶✾ ✶✶✴✷✵✶✾ ✵✻✴✷✵✷✵ ✵✷✴✷✵✷✺
❈♦✉♣♦♥
✾✪
✷✪
✶✶✪
✷✪
✹✪
✼✪
✷✪
✹✪
✼✪
✷✪
✼✪
✽✪
❆▼❨
✵✳✵✹✹
✵✳✵✹✾ ✵✳✵✺✸✾ ✵✳✵✺✼
✵✳✵✺✾ ✵✳✵✻✵✺ ✵✳✵✺✸✺ ✵✳✵✻✶✺
✵✳✵✻
✵✳✵✺✹
✵✳✵✻✺
✵✳✵✻✾
■ss✉❡ ❉❛t❡ ✷✵✵✹
✷✵✵✷
✷✵✵✸
✷✵✵✸
✷✵✵✹
✷✵✵✻
✷✵✵✾
✷✵✵✼
✷✵✵✽
✷✵✵✾
✷✵✵✺
✷✵✵✺
▼❛t✉r✐t② ✵✶✴✷✵✸✵ ✵✷✴✷✵✸✹ ✵✸✴✷✵✸✻ ✵✸✴✷✵✸✽
❈♦✉♣♦♥
✽✪
✽✪
✽✪
✹✪
❆▼❨
✵✳✵✼
✵✳✵✼✷
✵✳✵✼✷
✵✳✵✼✷
■ss✉❡ ❉❛t❡ ✷✵✵✵
✷✵✵✹
✷✵✵✻
✷✵✵✽
❚❛❜❧❡s
❚❤✐s t❛❜❧❡ ♣r❡s❡♥ts t❤❡ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❜♦♥❞ ❞❛t❛s❡t ❞♦✇♥❧♦❛❞❡❞ ❢r♦♠ ❉❛t❛str❡❛♠✳ ❲❡ ♣r♦✈✐❞❡ ✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡ ❛✈❡r❛❣❡ ♠✐❞ ②✐❡❧❞
❚❛❜❧❡ ✷✿
❉❡s❝r✐♣t✐✈❡ ❙t❛t✐st✐❝s ♦❢ t❤❡ ❇♦♥❞ ❛♥❞ ❈❉❙ ❇✐❞✲❆s❦ ❙♣r❡❛❞s
■♥ t❤✐s t❛❜❧❡✱ ✇❡ ♣r❡s❡♥t ❞❡s❝r✐♣t✐✈❡ st❛t✐st✐❝s ♦❢ t❤❡ ❜♦♥❞ ❛♥❞ ❈❉❙ ❇✐❞✲❆s❦ ❙♣r❡❛❞s ✭✐♥ ❜❛s✐s ♣♦✐♥ts✮
❛❝r♦ss t❤❡ t❡r♠ str✉❝t✉r❡ ❢♦r t❤❡ ✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs ♠❛t✉r✐t② ❢♦r ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✳
❋♦r s❛❦❡ ♦❢ ❝♦♠♣❛r✐s♦♥✱ ✇❡ ♥❡❡❞ t♦ ♠❛t❝❤ ❜♦♥❞ ♠❛t✉r✐t✐❡s t♦ ❈❉❙ ♠❛t✉r✐t✐❡s ✇❤✐❝❤ ❛r❡ ❝♦♥st❛♥t ♦✈❡r
t✐♠❡✳ ❚♦ ♣r♦①② ❢♦r t❤❡ ✶ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞✱ ✇❡ ✉s❡ t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❡ ❤❛✈❡ ❢♦r ❡❛❝❤
❝♦✉♥tr② ✭✐✳❡✳ ✵✷✴✷✵✶✸ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✽✴✷✵✶✶ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✻✴✷✵✶✶ ❢♦r ❚✉r❦❡②✮✳ ❚♦ ♣r♦①② t❤❡ ✸
②❡❛rs ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ✉s❡ ❜♦♥❞s t❤❛t ❡①♣✐r❡ r✐❣❤t ❛❢t❡r t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞s ✭✐✳❡✳ ✵✶✴✷✵✶✹
❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✶✷ ❢♦r ❇r❛③✐❧✱ ✵✶✴✷✵✶✸ ❢♦r ❚✉r❦❡②✮✳ ❋♦r t❤❡ ✺ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝❤♦♦s❡
❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❞♦ ♥♦t ❡①❝❡❡❞ ✷✵✶✺ ✭✐✳❡✳ ✵✸✴✷✵✶✺ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✸✴✷✵✶✺ ❢♦r ❇r❛③✐❧
❛♥❞ ✵✸✴✷✵✶✺ ❢♦r ❚✉r❦❡②✮✳ ❋♦r t❤❡ ✼ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ♣✐❝❦ ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t② ❞❛t❡s t❤❛t
❛r❡ ❛r♦✉♥❞ ✷✵✶✼ ✭✐✳❡✳ ✵✶✴✷✵✶✼ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✶✽ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✼✴✷✵✶✼ ❢♦r ❚✉r❦❡②✮✳ ❋✐♥❛❧❧②
t♦ ♣r♦①② ❢♦r t❤❡ ✶✵ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝♦❧❧❡❝t ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t✐❡s t❤❛t ❛r❡ ❛s ❝❧♦s❡ ❛s
♣♦ss✐❜❧❡ t♦ ✷✵✷✵ ✭✐✳❡✳ ✶✵✴✷✵✷✹ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✷✵ ❇r❛③✐❧ ❛♥❞ ✵✷✴✷✵✷✺ ❚✉r❦❡②✮✳ ❖✉r ❞❛t❛ s❡t r✉♥s
❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✵✴✵✾✴✷✵✶✵✳ ❚❤❡ t❛❜❧❡ s❤♦✇s t❤❡ ♠✐♥✱ ♠❛①✱ ♠❡❛♥ ❛♥❞ t❤❡ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥s ♦❢
t❤❡ ❜♦♥❞ ❛♥❞ ❈❉❙ ❜✐❞✲❛s❦ s♣r❡❛❞s ❛t ❡❛❝❤ ♠❛t✉r✐t②✳
✶❨
❇r❛③✐❧
▼✐♥
▼❛①
▼❡❛♥
❙t❞
P❤✐❧✐♣
▼✐♥
▼❛①
▼❡❛♥
❙t❞
❚✉r❦
▼✐♥
▼❛①
▼❡❛♥
❙t❞
✸❨
✺❨
✼❨
✶✵❨
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
✵
✷
✸✳✻✺
✶✳✾✾
✷✳✾✵
✶
✵✳✺✻
✶✳✼✹
✶✳✹✸
✶✳✻
✶✹✶✳✾✺
✻✶
✶✹✸✳✵✹
✹✵
✽✹✳✾✷
✹✶
✻✵✳✸✼
✷✼
✺✷✳✹✹
✸✵
✷✹✳✾✶
✽✳✸✶
✷✶✳✽✼
✻✳✾✽
✶✶✳✹✼
✹✳✶✽
✼✳✻✵
✻✳✵✾
✾✳✻✾
✺✳✽✷
✶✾✳✷✾
✻✳✶✷
✶✻✳✻✾
✹✳✷✹
✽✳✾✾
✸✳✹✸
✼✳✹✾
✸✳✷✹
✺✳✹✼
✷✳✾✷
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
✵✳✸✻
✹
✵
✸✳✺
✵
✶
✵
✵
✵
✸✳✷✾
✹✷✳✷
✶✵✷
✹✼✳✸✶
✽✻
✹✷✳✹✷
✺✵
✾✻✳✽✷
✻✵
✷✸✳✹✷
✺✺
✶✽✳✵✶
✶✾✳✵✻
✽✳✹✾
✶✹✳✷✺
✾✳✷✵
✽✳✵✸
✶✵✳✻✼
✶✶✳✽✻
✼✳✼✹
✶✶✳✵✽
✼✳✶✵
✶✻✳✶✵
✺✳✼✽
✶✵✳✶✽
✻✳✷✸
✼✳✵✼
✾✳✾✷
✼✳✾✶
✹✳✻✸
✼✳✾✻
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
✻✳✼✶
✷
✹✳✷✷
✷✳✸✶
✶✳✾✵
✶
✷✳✻✽
✶✳✼✺
✷✳✷✻
✶✳✺✾
✶✽✺✳✽✻
✶✸✻
✶✶✽✳✾✷
✼✺
✼✵✳✷✻
✺✵
✶✷✵✳✼✻
✹✹
✼✵✳✸✶
✺✵
✸✻✳✸✵
✶✺✳✻✺
✷✸✳✺✷
✶✵✳✷✷
✽✳✷✷
✺✳✺✺
✶✶✳✽✶
✼✳✽✻
✾✳✹✺
✽✳✸✷
✷✾✳✶✺
✶✼✳✽✵
✷✶✳✷✽
✾✳✻✾
✼✳✽✼
✻✳✻✺
✶✸✳✷✷
✻✳✸✽
✶✵✳✶✺
✼✳✸✺
✸✼
❚❛❜❧❡ ✸✿
Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s✿ ❈❉❙ ❉❛t❛
❚❤❡ t❛❜❧❡ ♣r❡s❡♥ts t❤❡ r❡s✉❧ts ♦❢ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ❛♥❛❧②s✐s ✭P❈❆✮ ❛❝r♦ss t❤❡ ❈❉❙ t❡r♠ str✉❝t✉r❡
❢♦r t❤❡ ✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs ♠❛t✉r✐t② ❢♦r ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✳ ❲❡ ✉s❡ t❤❡ ❈❉❙ ♠✐❞ q✉♦t❡s
❛♥❞ s♣❧✐t ♦✉r ❞❛t❛ s❡t ✐♥t♦ t✇♦ ♣❡r✐♦❞s✿ t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞ st❛rt✐♥❣ ❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽
❛♥❞ t❤❡ ❝r✐s✐s ♣❡r✐♦❞ st❛rt✐♥❣ ❢r♦♠ ✵✶✴✵✹✴✷✵✵✽ t♦ ✸✵✴✵✾✴✷✵✶✵✳ ■♥ P❛♥❡❧ ❆ ❛♥❞ P❛♥❡❧ ❇✱ ✇❡ s❤♦✇ t❤❡
r❡s✉❧s ♦❢ t❤❡ P❈❆ ❢♦r t❤❡ ♣r❡✲❝r✐s✐s ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞s r❡s♣❡❝t✐✈❡❧②✳
❈❉❙ ❉❛t❛
P❛♥❡❧ ❆
❋✸
✵✳✽✵
✲✵✳✹✶
✲✵✳✷✽
✵✳✵✷
✵✳✸✹
P❤✐❧✐♣♣✐♥❡s
❋✶ ❋✷
✵✳✶✺ ✵✳✼✺
✵✳✸✹ ✵✳✹✾
✵✳✹✾ ✵✳✵✽✻
✵✳✺✺ ✲✵✳✷✵
✵✳✺✺ ✲✵✳✸✽
❋✸
✵✳✻✷
✲✵✳✺✸
✲✵✳✹✶
✵✳✶✼
✵✳✸✺
✵✳✺✾ ✵✳✵✶ ✵✳✵✵
✾✻✳✼✷ ✷✳✺✺✺ ✵✳✸✸✵
✵✳✾✽ ✵✳✵✸ ✵✳✵✵
✾✻✳✼✷ ✷✳✾✺ ✵✳✶✼
✶✳✶✺ ✵✳✵✺
✾✹✳✽✽ ✹✳✻✵
✵✳✵✵
✵✳✸✽
❋❛❝t♦rs
✶②
✸②
✺②
✼②
✶✵②
❋✶ ❋✷ ❋✸
✵✳✺✷ ✵✳✻✽ ✲✵✳✺✵
✵✳✹✼ ✵✳✶✾ ✵✳✺✼
✵✳✹✹ ✲✵✳✶✺ ✵✳✹✸
✵✳✹✷ ✲✵✳✸✽ ✲✵✳✵✷
✵✳✸✾ ✲✵✳✺✼ ✲✵✳✺✵
❋✶ ❋✷ ❋✸
✵✳✸✽ ✵✳✽✷ ✵✳✸✼
✵✳✹✻ ✵✳✶✽ ✲✵✳✹✽
✵✳✹✼ ✲✵✳✶✸ ✲✵✳✺✷
✵✳✹✻ ✲✵✳✸✵ ✵✳✶✷
✵✳✹✺ ✲✵✳✹✷ ✵✳✺✽
❋✶ ❋✷ ❋✸
✵✳✹✺ ✵✳✼✺ ✲✵✳✸✼
✵✳✹✻ ✵✳✷✶ ✵✳✸✸
✵✳✹✺ ✲✵✳✶✼ ✵✳✻✹
✵✳✹✸ ✲✵✳✸✸ ✲✵✳✵✾
✵✳✹✷ ✲✵✳✺✶ ✲✵✳✺✼
❱❛r✐❛♥❝❡
Pr♦♣♦rt✐♦♥ ✭✪✮
✻✳✺✽ ✵✳✸✾ ✵✳✵✵
✾✹✳✷✸ ✺✳✻✺ ✵✳✵✻
✹✳✶✸ ✵✳✵✼✶ ✵✳✵✵
✾✽✳✶✶ ✶✳✻✼ ✵✳✶✹
✺✳✸✻ ✵✳✷✺ ✵✳✵✵
✾✺✳✷✷ ✹✳✺✼ ✵✳✶✻
❋❛❝t♦rs
✶②
✸②
✺②
✼②
✶✵②
❱❛r✐❛♥❝❡
Pr♦♣♦rt✐♦♥ ✭✪✮
P❛♥❡❧ ❇
❋✶
✵✳✷✺
✵✳✹✸
✵✳✹✾
✵✳✹✾
✵✳✺✶
❚✉r❦❡②
❋✷
✵✳✻✷
✵✳✺✹
✵✳✵✷
✲✵✳✸✵
✲✵✳✹✽
Pr❡✲❈r✐s✐s
❋✸
✲✵✳✹✺
✵✳✵✺
✵✳✻✻
✵✳✶✶
✲✵✳✺✼
❋✶
✵✳✵✸✶
✵✳✷✼
✵✳✹✼
✵✳✺✻
✵✳✻✶
❇r❛③✐❧
❋✷
✵✳✻✸
✵✳✺✾
✵✳✷✸
✲✵✳✵✽
✲✵✳✹✷
❉✉r✐♥❣ ❈r✐s✐s
✸✽
❚❛❜❧❡ ✹✿
Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s✿ ❇♦♥❞ ❉❛t❛
❚❤❡ t❛❜❧❡ ♣r❡s❡♥ts t❤❡ r❡s✉❧ts ♦❢ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ❛♥❛❧②s✐s ✭P❈❆✮ ❛❝r♦ss t❤❡ ❜♦♥❞ t❡r♠ str✉❝✲
t✉r❡ ❢♦r t❤❡ ✶✱ ✸✱ ✺✱ ✼ ❛♥❞ ✶✵ ②❡❛rs ♠❛t✉r✐t② ❢♦r ❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s ❛♥❞ ❚✉r❦❡②✳ ❋♦r s❛❦❡ ♦❢ ❝♦♠♣❛r✐s♦♥✱
✇❡ ♥❡❡❞ t♦ ♠❛t❝❤ ❜♦♥❞ ♠❛t✉r✐t✐❡s t♦ ❈❉❙ ♠❛t✉r✐t✐❡s ✇❤✐❝❤ ❛r❡ ❝♦♥st❛♥t ♦✈❡r t✐♠❡✳ ❚♦ ♣r♦①② ❢♦r t❤❡
✶ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞✱ ✇❡ ✉s❡ t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞ ✇❡ ❤❛✈❡ ❢♦r ❡❛❝❤ ❝♦✉♥tr② ✭✐✳❡✳ ✵✷✴✷✵✶✸ ❢♦r
P❤✐❧✐♣♣✐♥❡s✱ ✵✽✴✷✵✶✶ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✻✴✷✵✶✶ ❢♦r ❚✉r❦❡②✮✳ ❚♦ ♣r♦①② t❤❡ ✸ ②❡❛rs ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ✉s❡
❜♦♥❞s t❤❛t ❡①♣✐r❡ r✐❣❤t ❛❢t❡r t❤❡ s❤♦rt❡st ♠❛t✉r✐t② ❜♦♥❞s ✭✐✳❡✳ ✵✶✴✷✵✶✹ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✶✷ ❢♦r
❇r❛③✐❧✱ ✵✶✴✷✵✶✸ ❢♦r ❚✉r❦❡②✮✳ ❋♦r t❤❡ ✺ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ❝❤♦♦s❡ ❜♦♥❞s ✇✐t❤ ♠❛t✉r✐t② ❞❛t❡s t❤❛t
❞♦ ♥♦t ❡①❝❡❡❞ ✷✵✶✺ ✭✐✳❡✳ ✵✸✴✷✵✶✺ ❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✸✴✷✵✶✺ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✸✴✷✵✶✺ ❢♦r ❚✉r❦❡②✮✳ ❋♦r t❤❡
✼ ②❡❛r ♠❛t✉r✐t② ❜♦♥❞s✱ ✇❡ ♣✐❝❦ ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t② ❞❛t❡s t❤❛t ❛r❡ ❛r♦✉♥❞ ✷✵✶✼ ✭✐✳❡✳ ✵✶✴✷✵✶✼
❢♦r P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✶✽ ❢♦r ❇r❛③✐❧ ❛♥❞ ✵✼✴✷✵✶✼ ❢♦r ❚✉r❦❡②✮✳ ❋✐♥❛❧❧② t♦ ♣r♦①② ❢♦r t❤❡ ✶✵ ②❡❛r ♠❛t✉r✐t②
❜♦♥❞s✱ ✇❡ ❝♦❧❧❡❝t ❜♦♥❞s t❤❛t ❤❛✈❡ ♠❛t✉r✐t✐❡s t❤❛t ❛r❡ ❛s ❝❧♦s❡ ❛s ♣♦ss✐❜❧❡ t♦ ✷✵✷✵ ✭✐✳❡✳ ✶✵✴✷✵✷✹ ❢♦r
P❤✐❧✐♣♣✐♥❡s✱ ✵✶✴✷✵✷✵ ❇r❛③✐❧ ❛♥❞ ✵✷✴✷✵✷✺ ❚✉r❦❡②✮✳ ❲❡ s♣❧✐t ♦✉r ❞❛t❛ s❡t ✐♥t♦ t✇♦ ♣❡r✐♦❞s✿ t❤❡ ♣r❡
❝r✐s✐s ♣❡r✐♦❞ st❛rt✐♥❣ ❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽ ❛♥❞ t❤❡ ❝r✐s✐s ♣❡r✐♦❞ st❛rt✐♥❣ ❢r♦♠ ✵✶✴✵✹✴✷✵✵✽
t♦ ✸✵✴✵✾✴✷✵✶✵✳ ■♥ P❛♥❡❧ ❆ ❛♥❞ P❛♥❡❧ ❇✱ ✇❡ s❤♦✇ t❤❡ r❡s✉❧s ♦❢ t❤❡ P❈❆ ❢♦r t❤❡ ♣r❡✲❝r✐s✐s ❛♥❞ ❝r✐s✐s
♣❡r✐♦❞s r❡s♣❡❝t✐✈❡❧②✳
❇♦♥❞ ❉❛t❛
P❛♥❡❧ ❆
❋❛❝t♦rs
✶②
✸②
✺②
✼②
✶✵②
❱❛r✐❛♥❝❡
Pr♦♣♦rt✐♦♥ ✭✪✮
❋✶
✵✳✺✼
✵✳✺✹
✵✳✹✷
✵✳✸✷
✵✳✸✵
❚✉r❦❡②
❋✷ ❋✸
✲✵✳✸✻ ✲✵✳✻✻
✲✵✳✸✻ ✵✳✼✶
✵✳✵✽ ✲✵✳✵✾
✵✳✹✾ ✵✳✶✼
✵✳✻✽ ✲✵✳✵✽
Pr❡✲❈r✐s✐s
❋✶
✵✳✹✾
✵✳✹✾
✵✳✹✹
✵✳✷✺
✵✳✹✾
❇r❛③✐❧
❋✷ ❋✸
✲✵✳✺✹ ✲✵✳✶✺
✲✵✳✹✷ ✲✵✳✶✸
✵✳✷✸ ✵✳✹✹
✵✳✶✸ ✵✳✼✷
✵✳✻✼ ✲✵✳✹✾
P❤✐❧✐♣♣✐♥❡s
❋✶ ❋✷
✵✳✹✸ ✲✵✳✺✼
✵✳✹✹ ✲✵✳✸✻
✵✳✹✷ ✵✳✶✵
✵✳✹✼ ✵✳✵✽
✵✳✹✺ ✵✳✼✶
❋✸
✲✵✳✺✻
✵✳✶✼
✵✳✺✾
✵✳✷✼
✲✵✳✹✼
✶✳✵✾ ✵✳✵✼ ✵✳✵✵
✾✶✳✹✸ ✺✳✾✸ ✶✳✹✻
✶✳✼✺ ✵✳✵✽ ✵✳✵✵
✾✹✳✽✾ ✹✳✺✷ ✵✳✹✵
❋❛❝t♦rs
✶②
✸②
✺②
✼②
✶✵②
❋✶ ❋✷ ❋✸
✵✳✺✸ ✵✳✻✼ ✲✵✳✷✸
✵✳✺✶ ✵✳✶✸ ✲✵✳✵✶
✵✳✹✹ ✲✵✳✷✵ ✵✳✽✸
✵✳✸✻ ✲✵✳✹✻ ✲✵✳✷✽
✵✳✸✷ ✲✵✳✺✶ ✲✵✳✹✵
❋✶
✵✳✺✸
✵✳✺✼
✵✳✹✶
✵✳✷✻
✵✳✸✼
❋✸
✲✵✳✹✼
✵✳✹✶
✵✳✺✻
✲✵✳✵✽
✲✵✳✺✷
❋✶ ❋✷ ❋✸
✵✳✺✻ ✲✵✳✸✾ ✲✵✳✻✺
✵✳✹✾ ✲✵✳✸✾ ✵✳✻✼
✵✳✹✻ ✵✳✵✼ ✵✳✶✺
✵✳✸✼ ✵✳✺✹ ✲✵✳✷✸
✵✳✷✽ ✵✳✻✶ ✵✳✶✾
❱❛r✐❛♥❝❡
Pr♦♣♦rt✐♦♥ ✭✪✮
✶✹✳✶✽ ✵✳✶✻ ✵✳✵✹
✾✽✳✸✷ ✶✳✶✻ ✵✳✸✷
✽✳✹✹ ✵✳✸✷ ✵✳✵✷
✾✺✳✽ ✸✳✻✽ ✵✳✷✻
✶✶✳✻✶ ✵✳✷✷ ✵✳✵✺
✾✼✳✶✶ ✶✳✾✶ ✵✳✹✻
P❛♥❡❧ ❇
❉✉r✐♥❣ ❈r✐s✐s
✸✾
❋✷
✲✵✳✺✺
✲✵✳✷✾
✵✳✸✼
✵✳✸✵
✵✳✻✶
✶✳✽✹ ✵✳✵✸ ✵✳✵✶
✾✻✳✽✽ ✶✳✼✹ ✵✳✼✶
P❛r❛♠❡t❡r ❊st✐♠❛t✐♦♥ ♦❢ t❤❡ ❈■❘ Pr♦❝❡ss ❢♦r t❤❡ ❈❉❙ ▲✐q✉✐❞✐t② ❘✐s❦
Pr❡♠✐✉♠
❚❛❜❧❡ ✺✿
■♥ t❤✐s t❛❜❧❡✱ ✇❡ ♣r❡s❡♥t t❤❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ♣❛r❛♠❡t❡rs ✭✐♥ ♣❡r❝❡♥t❛❣❡ t❡r♠✮ ♦❢ t❤❡ ❈■❘ ♣r♦❝❡ss
r❡❧❡✈❛♥t t♦ y CDS (t) ✇❤✐❝❤ ✐s t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ r❡♣r❡s❡♥t✐♥❣ t❤❡ ❈❉❙ ❧✐q✉✐❞✐t② r✐s❦ ❞②♥❛♠✐❝s✳ α1
❝♦rr❡s♣♦♥❞s t♦ t❤❡ ♠❡❛♥ r❡✈❡rs✐♦♥ s♣❡❡❞✱ µ1 t❤❡ ♠❡❛♥ r❡✈❡rs✐♦♥ ❧❡✈❡❧✱ σ1 t❤❡ ✈♦❧❛t✐❧✐t② ❛♥❞ λ1 t❤❡
❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✭♦r ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦✮✳ ❚❤❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ st❛t❡ s♣❛❝❡ ❢♦r♠ ✐s ♣❡r❢♦r♠❡❞
✉s✐♥❣ t❤❡ ◗✉❛s✐ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞ ✭◗▼▲✮✳ ❲❡ s♣❧✐t ♦✉r s❛♠♣❧❡ ♣❡r✐♦❞ ✐♥ t✇♦ ♣❡r✐♦❞s✿ ❇❡❢♦r❡ ❈r✐s✐s
✭❇❈✮ ✭❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽✮ ❛♥❞ ❉✉r✐♥❣ ❈r✐s✐s ✭❉❈✮ ✭❢r♦♠ ✵✶✴✵✹✴✷✵✵✽ t♦ ✸✵✴✵✾✴✷✵✶✵✮✳
❚❤❡ ♣❛r❛♠❡t❡rs ε1 (i) r❡♣r❡s❡♥t t❤❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦rs ✐♥tr♦❞✉❝❡❞ ❢♦r ❡❛❝❤ ♠❛t✉r✐t② i ♦❢ t❤❡ ❈❉❙
❝♦♥tr❛❝t✳ ❲❡ ❝♦♠♣✉t❡ t❤❡ st❛♥❞❛r❞ ❡rr♦rs ✉s✐♥❣ t❤❡ ❲❤✐t❡ ♠❡t❤♦❞ ✭✶✾✽✷✮✳ ❋✐♥❛❧❧②✱ ∗∗∗ ❝♦rr❡s♣♦♥❞s t♦
✶✵✪ s✐❣♥✐✜❝❛♥❝❡ ❧❡✈❡❧ ✱ ∗∗ t♦ ✺✪ ❛♥❞ ∗ t♦ ✶✪✳
α1
µ1
σ1
λ1
ε1 (1)
ε1 (3)
ε1 (5)
ε1 (7)
ε1 (10)
▲♦❣✲▲✐❦
❇r❛③✐❧
❇❈
✶✹✳✵✼✼✯
❉❈
✸✺✳✹✷✵✯
P❤✐❧✐♣♣✐♥❡s
❇❈
❉❈
✷✳✼✼✽✯
✶✳✸✽✹✯
❚✉r❦❡②
❇❈
✶✳✺✶✽✯
❉❈
✹✳✻✷✾✯
✭✵✳✸✻✽✮
✭✷✳✽✵✽✮
✭✵✳✺✸✾✮
✭✵✳✶✷✻✮
✭✵✳✵✺✸✮
✭✵✳✶✺✽✮
✵✳✹✶✺✯
✵✳✵✽✺✷✯
✵✳✷✶✺✯
✶✳✹✹✻✯
✸✳✻✷✼✯
✹✳✹✸✷✯
✭✵✳✵✶✺✮
✭✵✳✵✵✶✮
✭✵✳✵✼✽✮
✭✵✳✶✷✸✮
✭✵✳✶✸✵✮
✭✵✳✷✷✶✮
✵✳✾✹✼✯✯✯
✶✺✳✽✵✷✯
✸✳✺✾✽✯✯
✹✶✳✵✻✻✯
✺✳✸✸✻✯
✸✾✳✽✷✺✯
✭✵✳✺✶✹✮
✭✷✳✶✷✮
✭✶✳✼✹✻✮
✭✵✳✵✼✹✮
✭✵✳✻✷✸✮
✭✵✳✻✾✸✮
✺✻✳✺✺✷✯
✸✶✳✽✼✸✯
✶✷✳✷✵✵✯
✸✾✳✷✼✽✯
✻✽✳✾✽✷✯
✸✽✳✹✺✶✯
✭✵✳✷✻✼✮
✭✵✳✾✺✾✮
✭✷✳✻✽✮
✭✵✳✷✶✾✮
✭✵✳✹✹✾✮
✭✵✳✷✷✽✮
✺✻✳✽✺✽✯
✶✾✳✻✹✽✯
✶✷✳✽✸✶✯
✹✵✳✾✼✾✯
✸✳✾✵✺✯
✻✳✷✷✽✯
✭✶✳✷✻✷✮
✭✵✳✾✽✼✮
✭✶✳✸✻✻✮
✭✵✳✶✾✸✮
✭✵✳✹✶✷✮
✭✵✳✷✹✶✮
✽✳✺✺✾✯
✼✳✽✷✵✯
✸✳✾✺✸✯✯✯
✸✾✳✾✶✹✯
✶✳✻✻✻✯
✺✳✹✷✺✯
✭✶✳✵✹✹✮
✭✵✳✾✻✵✮
✭✷✳✸✽✷✮
✭✵✳✵✷✽✮
✭✵✳✷✵✷✮
✭✵✳✶✼✺✮
✸✳✸✷✵✯
✹✳✵✵✷✯
✽✳✹✻✵✯
✸✾✳✸✷✵✯
✷✳✼✷✶✯
✺✳✷✷✸✯
✭✶✳✸✻✷✮
✭✵✳✽✶✹✮
✭✶✳✷✷✸✮
✭✵✳✵✸✻✮
✭✵✳✸✷✺✮
✭✶✳✶✺✹✮
✷✳✽✽✼✯
✸✳✶✽✺✯
✸✳✷✶✵
✸✾✳✹✻✶✯
✷✳✹✺✷✯
✺✳✸✷✷✯
✭✵✳✹✼✾✮
✭✵✳✺✷✻✮
✭✺✳✷✻✻✮
✭✵✳✵✺✻✮
✭✵✳✶✽✻✮
✭✶✳✽✹✻✮
✷✳✸✵✾✯
✸✳✵✽✺✯
✷✳✸✻✵✯
✸✾✳✺✽✶✯
✶✳✼✺✻✯
✺✳✸✷✷✯
✭✵✳✺✺✸✺✮
✭✵✳✺✸✷✮
✭✵✳✺✷✸✮
✭✵✳✵✼✷✮
✭✵✳✷✷✷✮
✭✶✳✹✼✻✮
✻✻✹✻✳✹
✼✹✻✽✳✾
✻✾✾✶✳✷
✶✵✾✺✻
✺✽✸✵✳✽
✷✾✶✻✷
✹✵
P❛r❛♠❡t❡r ❊st✐♠❛t✐♦♥ ♦❢ t❤❡ ❈■❘ Pr♦❝❡ss ❢♦r t❤❡ ❇♦♥❞ ▲✐q✉✐❞✐t② ❘✐s❦
Pr❡♠✐✉♠
❚❛❜❧❡ ✻✿
■♥ t❤✐s t❛❜❧❡✱ ✇❡ ♣r❡s❡♥t t❤❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ♣❛r❛♠❡t❡rs ✭✐♥ ♣❡r❝❡♥t❛❣❡ t❡r♠✮ ♦❢ t❤❡ ❈■❘ ♣r♦❝❡ss
r❡❧❡✈❛♥t t♦ y bond (t) ✇❤✐❝❤ ✐s t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ r❡♣r❡s❡♥t✐♥❣ t❤❡ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ ❞②♥❛♠✐❝s✳ α2
❝♦rr❡s♣♦♥❞s t♦ t❤❡ ♠❡❛♥ r❡✈❡rs✐♦♥ s♣❡❡❞✱ µ2 t❤❡ ♠❡❛♥ r❡✈❡rs✐♦♥ ❧❡✈❡❧✱ σ2 t❤❡ ✈♦❧❛t✐❧✐t② ❛♥❞ λ2 t❤❡
❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✭♦r ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦✮✳ ❚❤❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ st❛t❡ s♣❛❝❡ ❢♦r♠ ✐s ♣❡r❢♦r♠❡❞
✉s✐♥❣ t❤❡ ◗✉❛s✐ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞ ✭◗▼▲✮✳ ❲❡ s♣❧✐t ♦✉r s❛♠♣❧❡ ♣❡r✐♦❞ ✐♥ t✇♦ ♣❡r✐♦❞s✿ ❇❡❢♦r❡ ❈r✐s✐s
✭❇❈✮ ✭❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽✮ ❛♥❞ ❉✉r✐♥❣ ❈r✐s✐s ✭❉❈✮ ✭❢r♦♠ ✵✶✴✵✹✴✷✵✵✽ t♦ ✸✵✴✵✾✴✷✵✶✵✮✳
❚❤❡ ♣❛r❛♠❡t❡rs ε2 (i) r❡♣r❡s❡♥t t❤❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦rs ✐♥tr♦❞✉❝❡❞ ❢♦r ❡❛❝❤ ♠❛t✉r✐t② i ♦❢ t❤❡ ❈❉❙
❝♦♥tr❛❝t✳ ❲❡ ❝♦♠♣✉t❡ t❤❡ st❛♥❞❛r❞ ❡rr♦rs ✉s✐♥❣ t❤❡ ❲❤✐t❡ ♠❡t❤♦❞ ✭✶✾✽✷✮✳ ❋✐♥❛❧❧②✱ ∗∗∗ ❝♦rr❡s♣♦♥❞s t♦
✶✵✪ s✐❣♥✐✜❝❛♥❝❡ ❧❡✈❡❧ ✱ ∗∗ t♦ ✺✪ ❛♥❞ ∗ t♦ ✶✪✳
α2
µ2
σ2
λ2
ε2 (1)
ε2 (3)
ε2 (5)
ε2 (7)
ε2 (10)
▲♦❣✲▲✐❦
❇r❛③✐❧
❇❈
✷✳✾✶✻✯
❉❈
✶✳✷✵✺✯
P❤✐❧✐♣♣✐♥❡s
❇❈
❉❈
✾✳✷✹✺✯
✶✶✳✵✽✾✯
❚✉r❦❡②
❇❈
✹✾✳✼✻✷✯
✭✵✳✶✺✼✮
✭✵✳✵✸✾✮
✭✵✳✸✶✹✮
✭✵✳✶✼✻✮
✭✵✳✸✷✹✮
✭✶✳✷✼✼✮
✷✳✷✼✼✯
✶✳✹✵✾✯
✵✳✺✵✾✯
✵✳✷✷✶✯
✵✳✵✹✶✯
✵✳✸✸✺✯
✭✵✳✷✸✼✮
✭✵✳✵✸✾✮
✭✵✳✵✶✹✮
✭✵✳✵✵✶✮
✭✵✳✵✵✽✮
✭✵✳✵✶✸✮
✹✸✳✻✽✽✯
✻✳✾✶✺✯
✶✺✳✺✾✵✯
✷✳✺✽✹✯
✵✳✾✹✸
✷✵✳✻✺✺✯
❉❈
✽✳✾✾✷✯
✭✵✳✸✼✹✮
✭✵✳✹✽✼✮
✭✵✳✺✵✸✮
✭✵✳✵✾✺✮
✭✵✳✾✺✵✮
✭✵✳✻✼✵✮
✸✶✳✽✼✶✯
✻✾✳✵✷✹✯
✺✽✳✶✹✼✯
✺✾✳✻✽✶✯
✷✵✳✻✵✵✯
✺✺✳✻✵✾✯
✭✵✳✻✷✵✮
✭✵✳✺✽✾✵✮
✭✵✳✻✺✻✮
✭✵✳✸✼✹✮
✭✵✳✺✺✻✮
✭✵✳✹✽✶✮
✹✻✳✹✼✯
✺✾✳✸✺✻✯
✹✶✳✷✷✯
✹✶✳✶✾✸✯
✷✻✳✶✵✾✯
✷✼✳✺✵✷✯
✭✶✳✵✻✺✮
✭✶✳✷✾✺✮
✭✵✳✸✾✷✮
✭✵✳✹✹✼✮
✭✶✳✷✽✾✮
✭✵✳✹✻✸✮
✼✺✳✾✷✯
✹✹✳✹✹✼✯
✶✳✽✶✶✯
✸✵✳✼✽✶✯
✷✸✳✻✺✸✯
✷✶✳✶✹✯
✭✵✳✸✾✺✮
✭✺✳✼✽✹✮
✭✵✳✸✷✸✮
✭✵✳✵✹✾✮
✭✵✳✹✸✸✮
✭✵✳✷✻✻✮
✺✾✳✵✺✶✯
✹✾✳✼✵✻✯
✶✳✽✾✶✯
✸✷✳✾✺✵✯
✾✳✾✵✺✯
✷✶✳✾✽✯
✭✵✳✺✽✾✮
✭✷✳✽✹✺✮
✭✵✳✶✹✵✮
✭✵✳✵✽✵✮
✭✵✳✹✻✸✮✯
✭✵✳✻✶✻✮
✸✳✸✽✷✯
✺✶✳✹✺✷✯
✵✳✻✹✺✯
✹✸✳✵✽✼✯
✵✳✻✵✸✯
✷✹✳✽✼✯
✭✵✳✷✷✼✮
✭✵✳✼✷✺✮
✭✵✳✶✶✵✮
✭✵✳✶✺✺✮
✭✵✳✵✶✸✮
✭✵✳✺✻✸✮
✸✻✳✸✸✷✯
✹✽✳✼✵✶✯
✷✳✾✻✾✯
✷✻✳✼✽✻✯
✶✳✶✷✾
✷✽✳✽✵✯
✭✵✳✽✶✼✮
✭✶✳✹✶✹✮
✭✵✳✷✼✹✮
✭✵✳✶✵✻✮
✭✵✳✽✼✸✮
✭✵✳✶✼✸✮
✽✻✸✾✳✷
✶✶✾✽✹
✻✶✵✸✳✵
✾✼✽✽✳✶
✹✻✻✼✳✹
✷✸✹✶✵
✹✶
❚❛❜❧❡ ✼✿ ❉❡s❝r✐♣t✐✈❡ ❙t❛t✐st✐❝s ♦❢ t❤❡ ❇♦♥❞ ❛♥❞ ❈❉❙ ❚✐♠❡✲❱❛r②✐♥❣ ▲✐q✉✐❞✐t② ❘✐s❦
Pr❡♠✐✉♠
■♥ t❤✐s t❛❜❧❡✱ ✇❡ ♣r❡s❡♥t t❤❡ ❞❡s❝r✐♣t✐✈❡ st❛t✐st✐❝s ♦❢ t❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡ t✐♠❡✲✈❛r②✐♥❣ ❈❉❙ ❛♥❞ ❜♦♥❞
❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ✭∆(y CDS (t)
❇r❛③✐❧✱ P❤✐❧✐♣♣✐♥❡s
y
(t) ❛♥❞
❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦
λ1 ❛♥❞ λ2 ❛r❡ t❤❡ ♠❛r❦❡t ♣r✐❝❡s ♦❢ r✐s❦ ♦❢ ❜♦t❤ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts r❡s♣❡❝t✐✈❡❧②✳
❛♥❞ ❚✉r❦❡② ✇❤❡r❡
r❡s♣❡❝t✐✈❡❧② ❛♥❞
CDS
∗ λ1 ) ❛♥❞ ∆(y bond (t) ∗ λ2 ) r❡s♣❡❝t✐✈❡❧②✮ ❢♦r
y bond (t)✮ ❛r❡ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡s ♦❢ t❤❡ ❈❉❙ ❛♥❞
❚❤❡ t❛❜❧❡ s❤♦✇s t❤❡ ♠✐♥✱ ♠❛①✱ ♠❡❛♥ ❛♥❞ t❤❡ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥s ❢♦r t❤❡ ♣r❡✲❝r✐s✐s ♣❡r✐♦❞ ✭✐✳❡✳ ❢r♦♠
✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽✮ ❛♥❞ t❤❡ ❝r✐s✐s ♣❡r✐♦❞ ✭✐✳❡✳ ❢r♦♠ ✵✶✴✵✹✴✷✵✵✽ t♦ ✸✵✴✵✾✴✷✵✶✵✮✳
Pr❡✲❈r✐s✐s
❇r❛③✐❧
▼✐♥
▼❛①
▼❡❛♥
❙t❞
P❤✐❧✐♣
▼✐♥
▼❛①
▼❡❛♥
❙t❞
❚✉r❦
▼✐♥
▼❛①
▼❡❛♥
❙t❞
❈r✐s✐s
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
✲✶✸✹✳✻✵
✲✵✳✵✷✹
✲✶✻✵✳✵✵
✲✵✳✷✷✽
✶✶✹✳✻✾
✵✳✵✵✼✶
✶✶✺✳✹✺
✵✳✶✵✵
✵✳✵✺✼✼
✲✽✳✷✷❡❫✲✺
✵✳✷✵✶
✵✳✵✵✶✷
✷✵✳✻✼
✵✳✵✵✸
✸✶✳✶✹
✵✳✵✸✽
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
✲✷✸✷✳✸✾
✲✷✳✵✻✷✶
✲✵✳✵✸✶
✲✸✵✸✾✳✽
✺✸✳✼✾
✵✳✺✾✺✷
✵✳✵✷✼✹
✶✼✷✶✳✶
✶✳✸✶✾
✵✳✵✵✶✾
✹✳✵✾✽❡❫✲✹
✷✵✳✷✷
✷✹✳✾✺
✵✳✸✶✼
✵✳✵✵✼✺
✸✸✼✳✾✶
❇♦♥❞
❈❉❙
❇♦♥❞
❈❉❙
✲✶✳✸✼✸❡❫✲✹
✲✹✽✷✳✷✾
✲✷✳✹✽
✲✺✺✵✳✼✽
✺✳✻✾❡❫✲✺
✶✶✹✳✾✽
✵✳✺✶✼
✼✺✽✳✷✵
✲✶✳✷✷❡❫✲✻
✲✵✳✷✷✵
✲✵✳✵✷✹✾
✵✳✸✼✺
✶✳✽✻❡❫✲✺
✻✽✳✹✵
✵✳✷✽✸
✽✻✳✽✶
✹✷
❚❛❜❧❡ ✽✿
●r❛♥❣❡r✲❈❛✉s❛❧✐t② ❆♥❛❧②s✐s
■♥ t❤✐s t❛❜❧❡✱ ✇❡ r❡♣♦rt t❤❡ r❡s✉❧ts ♦❢ t❤❡ ●r❛♥❣❡r ❈❛✉s❛❧✐t② ❆♥❛❧②s✐s ❜❡t✇❡❡♥ t❤❡ ❝❤❛♥❣❡s ♦❢ t❤❡
t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠ ❢♦r t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts ✭△ACDS (t) = △(y CDS (t) ∗ λ1 )
❛♥❞ △ABond (t) = △(y bond (t) ∗ λ2 ) r❡s♣❡❝t✐✈❡❧②✮ ❛♥❞ ❢♦r ❡❛❝❤ ♦❢ ❇r❛③✐❧✱ ❚✉r❦❡② ❛♥❞ P❤✐❧✐♣♣✐♥❡s ✇❤❡r❡
y CDS (t) ❛♥❞ y bond (t)✮ ❛r❡ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡s ♦❢ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ❧✐q✉✐❞✐t② r✐s❦ r❡s♣❡❝t✐✈❡❧② ❛♥❞ λ1
❛♥❞ λ2 ❛r❡ t❤❡ ♠❛r❦❡t ♣r✐❝❡s ♦❢ r✐s❦ ♦❢ ❜♦t❤ t❤❡ ❈❉❙ ❛♥❞ ❜♦♥❞ ♠❛r❦❡ts r❡s♣❡❝t✐✈❡❧②✳ ❲❡ ❛♣♣❧② t❤❡
●r❛♥❣❡r✲❈❛✉s❛❧✐t② ✭●❈✮ t❡st ✐♥ ♦r❞❡r t♦ ✜♥❞ ✇❤✐❝❤ ♠❛r❦❡t ❧❡❛❞s t❤❡ ♦t❤❡r ✐♥ t❡r♠s ♦❢ ♣r✐❝❡ ❞✐s❝♦✈❡r②✳
❲❤❡♥ t❤❡ ❋✲st❛t ✐s s✐❣♥✐✜❝❛♥t t❤✐s ♠❡❛♥s t❤❛t ✇❡ ❝❛♥♥♦t r❡❥❡❝t t❤❡ ❢❛❝t t❤❛t t❤❡ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡
❝❛♥♥♦t ❣r❛♥❣❡r ❝❛✉s❡ t❤❡ ❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡✳ ■♥ ♦✉r ❛♥❛❧②s✐s✱ ✇❡ s♣❧✐t ♦✉r s❛♠♣❧❡ ✐♥ t✇♦ ♣❡r✐♦❞s ✭♣r❡✲
❝r✐s✐s ♣❡r✐♦❞ ❢r♦♠ ✵✶✴✶✶✴✷✵✵✺ t♦ ✸✶✴✵✸✴✷✵✵✽ ❛♥❞ ❝r✐s✐s ♣❡r✐♦❞ ❢r♦♠ ✵✶✴✵✹✴✷✵✵✽ t♦ ✸✵✴✵✾✴✷✵✶✵✮ ❛♥❞
♣r❡s❡♥t t❤❡ ●❈ ❛♥❛❧②s✐s ❢♦r ✉♣ t♦ ✸ ❧❛❣s✳ ✯ ❛♥❞ ✯✯ r❡❢❡rs t♦ ✶✪ ❛♥❞ ✺✪ s✐❣♥✐✜❝❛♥❝❡ ❧❡✈❡❧ r❡s♣❡❝t✐✈❡❧②✳
◆♦t❡ t❤❛t ✐❢ ❋ ❃ ❈❱ ✇❡ r❡❥❡❝t t❤❡ ♥✉❧❧ ❤②♣♦t❤❡s✐s t❤❛t t❤❡ ❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡ ❞♦❡s ♥♦t ●r❛♥❣❡r ❈❛✉s❡
t❤❡ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡ ✇❤❡r❡ ❈❱ st❛♥❞s ❢♦r t❤❡ ❝r✐t✐❝❛❧ ✈❛❧✉❡✳ △ABond (t) ❛♥❞ △ACDS (t) st❛♥❞ ❢♦r
t❤❡ ❝❤❛♥❣❡s ♦❢ ❜♦♥❞ ❛♥❞ ❈❉❙ t✐♠❡✲✈❛r②✐♥❣ ❧✐q✉✐❞✐t② r✐s❦ ♣r❡♠✐✉♠✳
❇r❛③✐❧
P❤✐❧✐♣♣✐♥❡s
❚✉r❦❡②
❇❡❢♦r❡ ❈r✐s✐s
●❈ ✭❋✲st❛t✮✲❧❛❣ ✶
●❈ ✭❋✲st❛t✮✲❧❛❣ ✷
●❈ ✭❋✲st❛t✮✲❧❛❣ ✸
△ABond (t)
△ACDS (t)
△ABond (t)
△ACDS (t)
△ABond (t)
△ACDS (t)
❋❃❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
✽✳✽✶✯
✾✳✵✺✯
✸✸✳✾✻✯
✺✶✳✸✺✯
✷✶✳✷✸✯
✹✳✺✻✯✯
❋❁❈❱
❋❁❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
✷✳✾✸
✸✳✸✻
✶✻✳✹✶✯
✹✸✳✽✾✯
✷✵✳✻✻✯
✸✳✽✶✯✯
❋❃❈❱
❋❁❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
❋❃❈❱
✺✳✸✵✯✯
✸✳✼✼
✽✳✸✾✯
✸✾✯
✷✻✳✼✶✯
✸✳✽✶✯✯
❉✉r✐♥❣ ❈r✐s✐s
●❈ ✭❋✲st❛t✮✲❧❛❣ ✶
●❈ ✭❋✲st❛t✮✲❧❛❣ ✷
●❈ ✭❋✲st❛t✮✲❧❛❣ ✸
△ABond (t)
△ACDS (t)
△ABond (t)
△ACDS (t)
△ABond (t)
△ACDS (t)
❋❃❈❱
❋❃❈❱
❋❁❈❱
❋❁❈❱
❋❃❈❱
❋❁❈❱
✷✻✳✾✾✯
✺✳✾✸✯✯
✵✳✹✷
✵✳✵✹✼
✷✷✳✻✸✯
✷✳✹
❋❃❈❱
❋❃❈❱
❋❁❈❱
❋❁❈❱
❋❃❈❱
❋❃❈❱
✷✵✳✻✺✯
✺✳✵✽✯✯
✵✳✹✹
✵✳✵✺
✺✵✳✺✶✯
✸✸✳✽✻✯
❋❃❈❱
❋❃❈❱
❋❁❈❱
❋❁❈❱
❋❃❈❱
❋❃❈❱
✷✵✳✻✺✯
✹✳✼✹✯✯
✵✳✸✻
✵✳✵✷
✶✺✳✷✼✯
✻✻✳✷✹✯
✹✸
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