In the standard approach to fund valuation, it is often assumed that markets are perfectly liquid... more In the standard approach to fund valuation, it is often assumed that markets are perfectly liquid and hence assets have unique prices. In practice, however, as has been widely documented, this is not the case. Asset values are impacted by deterioration of market liquidity (market depth). However, the work by Acerbi and Scandolo (Quantitative Finance, 2008, 8(7), 681) highlighted, in addition, the key role that the liquidity policies of the fund can have on the fund value. Funds with the identical positions but differing liquidity policies have different values. In this paper, we describe and analyze, the relationship between the fund value and the liquidity policy (constraints that can potentially be called upon, and that are imposed externally on the fund manager). These constraints, for example, can be a requirement to be able to generate an amount of cash (due to possible adverse redemption), a minimum weight requirement per asset, or a market risk constraint such as a maximum expected shortfall (ES). In this paper we employ a Power-Law Marginal Supply-Demand Curves (MSDCs) to model market depth, together with various types of liquidity policies. These liquidity restrictions affect, to a varying degree, the liquidation process of illiquid and high volatility assets. We find that as the liquidity policy becomes stricter with the portfolio ES constraint, the liquidity costs increase significantly.
In this thesis I quantify the potential cost of liquidity constraints on a long equity portfolio ... more In this thesis I quantify the potential cost of liquidity constraints on a long equity portfolio using the liquidity risk framework of Acerbi and Scandolo (2008). The model modifies the classical mark-to-market valuation model, and incorporates the impact of liquidity policies of portfolios on the liquidity adjustment valuation (LVA). Also, I suggest a quantitative indicator that scores market liquidity ranging from 0 to 1 (perfect liquidity) for a portfolio with possible liquidity constraints.
The thesis consists of three major studies. In the first one, I compute LVA given the liquidity policy. Cash, minimum weight and portfolio expected shortfall (ES) liquidity policies on a long equity portfolio are formulated and combined to quantify the portfolio liquidity risk in the presence of liquidity constraints. Several numerical examples in the results demonstrate the importance associated the incorporation of the liquidity policy in the liquidity risk valuation.
In the second study, I employ the transaction costs measure of Garleanu and Pedersen (2013) and the optimal execution paradigm of Almgren and Chriss (2000) to quantify the execution costs and the revenue risk terms incurred when implementing the trading strategies over multiple periods. The measure of market depth in the model of Garleanu and Pedersen (2013) is calibrated using the Power-Law marginal supply and demand curves (MSDCs). The results are compared with the portfolio liquidity costs estimated from the liquidity risk measure of Finger (2011).
Finally, in the third study, I estimate the liquidity-adjusted portfolio ES for a long equity portfolio with the liquidity constraints. Portfolio pure market P&L scenarios are based on initial positions, and the liquidity adjustments are based on positions of the portfolio sold, which depends on the specified liquidity constraints. Portfolio pure market P&L scenarios
and state-dependent liquidity adjustments are integrated to obtain liquidity-adjusted P&L scenarios. Then, I apply the liquidity score method (Meucci, 2012) on the liquidity-plus-market P&L distribution to quantify the market liquidity for the portfolio.
The results in the thesis show the importance of pricing liquidity risk with liquidity constraints. The liquidity costs can vary greatly according to different liquidity policies, portfolio MtM values, market situation and time to liquidation.
In this report, a prototype pricing system for the arithmetic Asian option is developed with the ... more In this report, a prototype pricing system for the arithmetic Asian option is developed with the use of QuantLib and FpML. It is believed that Asian options have effective risk management features because the spot prices of the underlying are averaged over time. When the new pricing engine is added by extending the QuantLib architecture, Boyle’s High-precision model (2006) is employed to value a short time arithmetic Asian contingent claim. Moreover, FpML interface, which can be used to automate OTC trades, is implemented to match with the QuantLib pricing functionality. FpML schema has been extended to deal with pricing details such as calculation method as an input and error estimate as an output for the QuantLib. There is credibility that the option prices from Boyle’s formula for the
large σ^2 T agree with the values computed from Monte Carlo simulation; however, as the time duration decreases, there is some discrepancy in the prices between them caused by extreme oscillation in ψr(y,τ) of the Boyle model.
In the standard approach to fund valuation, it is often assumed that markets are perfectly liquid... more In the standard approach to fund valuation, it is often assumed that markets are perfectly liquid and hence assets have unique prices. In practice, however, as has been widely documented, this is not the case. Asset values are impacted by deterioration of market liquidity (market depth). However, the work by Acerbi and Scandolo (Quantitative Finance, 2008, 8(7), 681) highlighted, in addition, the key role that the liquidity policies of the fund can have on the fund value. Funds with the identical positions but differing liquidity policies have different values. In this paper, we describe and analyze, the relationship between the fund value and the liquidity policy (constraints that can potentially be called upon, and that are imposed externally on the fund manager). These constraints, for example, can be a requirement to be able to generate an amount of cash (due to possible adverse redemption), a minimum weight requirement per asset, or a market risk constraint such as a maximum expected shortfall (ES). In this paper we employ a Power-Law Marginal Supply-Demand Curves (MSDCs) to model market depth, together with various types of liquidity policies. These liquidity restrictions affect, to a varying degree, the liquidation process of illiquid and high volatility assets. We find that as the liquidity policy becomes stricter with the portfolio ES constraint, the liquidity costs increase significantly.
In this thesis I quantify the potential cost of liquidity constraints on a long equity portfolio ... more In this thesis I quantify the potential cost of liquidity constraints on a long equity portfolio using the liquidity risk framework of Acerbi and Scandolo (2008). The model modifies the classical mark-to-market valuation model, and incorporates the impact of liquidity policies of portfolios on the liquidity adjustment valuation (LVA). Also, I suggest a quantitative indicator that scores market liquidity ranging from 0 to 1 (perfect liquidity) for a portfolio with possible liquidity constraints.
The thesis consists of three major studies. In the first one, I compute LVA given the liquidity policy. Cash, minimum weight and portfolio expected shortfall (ES) liquidity policies on a long equity portfolio are formulated and combined to quantify the portfolio liquidity risk in the presence of liquidity constraints. Several numerical examples in the results demonstrate the importance associated the incorporation of the liquidity policy in the liquidity risk valuation.
In the second study, I employ the transaction costs measure of Garleanu and Pedersen (2013) and the optimal execution paradigm of Almgren and Chriss (2000) to quantify the execution costs and the revenue risk terms incurred when implementing the trading strategies over multiple periods. The measure of market depth in the model of Garleanu and Pedersen (2013) is calibrated using the Power-Law marginal supply and demand curves (MSDCs). The results are compared with the portfolio liquidity costs estimated from the liquidity risk measure of Finger (2011).
Finally, in the third study, I estimate the liquidity-adjusted portfolio ES for a long equity portfolio with the liquidity constraints. Portfolio pure market P&L scenarios are based on initial positions, and the liquidity adjustments are based on positions of the portfolio sold, which depends on the specified liquidity constraints. Portfolio pure market P&L scenarios
and state-dependent liquidity adjustments are integrated to obtain liquidity-adjusted P&L scenarios. Then, I apply the liquidity score method (Meucci, 2012) on the liquidity-plus-market P&L distribution to quantify the market liquidity for the portfolio.
The results in the thesis show the importance of pricing liquidity risk with liquidity constraints. The liquidity costs can vary greatly according to different liquidity policies, portfolio MtM values, market situation and time to liquidation.
In this report, a prototype pricing system for the arithmetic Asian option is developed with the ... more In this report, a prototype pricing system for the arithmetic Asian option is developed with the use of QuantLib and FpML. It is believed that Asian options have effective risk management features because the spot prices of the underlying are averaged over time. When the new pricing engine is added by extending the QuantLib architecture, Boyle’s High-precision model (2006) is employed to value a short time arithmetic Asian contingent claim. Moreover, FpML interface, which can be used to automate OTC trades, is implemented to match with the QuantLib pricing functionality. FpML schema has been extended to deal with pricing details such as calculation method as an input and error estimate as an output for the QuantLib. There is credibility that the option prices from Boyle’s formula for the
large σ^2 T agree with the values computed from Monte Carlo simulation; however, as the time duration decreases, there is some discrepancy in the prices between them caused by extreme oscillation in ψr(y,τ) of the Boyle model.
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Papers by Hwayoung Lee
The thesis consists of three major studies. In the first one, I compute LVA given the liquidity policy. Cash, minimum weight and portfolio expected shortfall (ES) liquidity policies on a long equity portfolio are formulated and combined to quantify the portfolio liquidity risk in the presence of liquidity constraints. Several numerical examples in the results demonstrate the importance associated the incorporation of the liquidity policy in the liquidity risk valuation.
In the second study, I employ the transaction costs measure of Garleanu and Pedersen (2013) and the optimal execution paradigm of Almgren and Chriss (2000) to quantify the execution costs and the revenue risk terms incurred when implementing the trading strategies over multiple periods. The measure of market depth in the model of Garleanu and Pedersen (2013) is calibrated using the Power-Law marginal supply and demand curves (MSDCs). The results are compared with the portfolio liquidity costs estimated from the liquidity risk measure of Finger (2011).
Finally, in the third study, I estimate the liquidity-adjusted portfolio ES for a long equity portfolio with the liquidity constraints. Portfolio pure market P&L scenarios are based on initial positions, and the liquidity adjustments are based on positions of the portfolio sold, which depends on the specified liquidity constraints. Portfolio pure market P&L scenarios
and state-dependent liquidity adjustments are integrated to obtain liquidity-adjusted P&L scenarios. Then, I apply the liquidity score method (Meucci, 2012) on the liquidity-plus-market P&L distribution to quantify the market liquidity for the portfolio.
The results in the thesis show the importance of pricing liquidity risk with liquidity constraints. The liquidity costs can vary greatly according to different liquidity policies, portfolio MtM values, market situation and time to liquidation.
large σ^2 T agree with the values computed from Monte Carlo simulation; however, as the time duration decreases, there is some discrepancy in the prices between them caused by extreme oscillation in ψr(y,τ) of the Boyle model.
The thesis consists of three major studies. In the first one, I compute LVA given the liquidity policy. Cash, minimum weight and portfolio expected shortfall (ES) liquidity policies on a long equity portfolio are formulated and combined to quantify the portfolio liquidity risk in the presence of liquidity constraints. Several numerical examples in the results demonstrate the importance associated the incorporation of the liquidity policy in the liquidity risk valuation.
In the second study, I employ the transaction costs measure of Garleanu and Pedersen (2013) and the optimal execution paradigm of Almgren and Chriss (2000) to quantify the execution costs and the revenue risk terms incurred when implementing the trading strategies over multiple periods. The measure of market depth in the model of Garleanu and Pedersen (2013) is calibrated using the Power-Law marginal supply and demand curves (MSDCs). The results are compared with the portfolio liquidity costs estimated from the liquidity risk measure of Finger (2011).
Finally, in the third study, I estimate the liquidity-adjusted portfolio ES for a long equity portfolio with the liquidity constraints. Portfolio pure market P&L scenarios are based on initial positions, and the liquidity adjustments are based on positions of the portfolio sold, which depends on the specified liquidity constraints. Portfolio pure market P&L scenarios
and state-dependent liquidity adjustments are integrated to obtain liquidity-adjusted P&L scenarios. Then, I apply the liquidity score method (Meucci, 2012) on the liquidity-plus-market P&L distribution to quantify the market liquidity for the portfolio.
The results in the thesis show the importance of pricing liquidity risk with liquidity constraints. The liquidity costs can vary greatly according to different liquidity policies, portfolio MtM values, market situation and time to liquidation.
large σ^2 T agree with the values computed from Monte Carlo simulation; however, as the time duration decreases, there is some discrepancy in the prices between them caused by extreme oscillation in ψr(y,τ) of the Boyle model.