Co-Founder and CTO at Lacima Group, PhD Computer Science from University of Warwick, BSc Honours 1st Class Astrophysics from University of Birmingham Address: Sydney
In this paper we discuss the use of mathematical programming techniques linear, dynamic, and goal... more In this paper we discuss the use of mathematical programming techniques linear, dynamic, and goal programming to the problem of the risk management of derivative securities (also known as contingent claims or options). We focus on the problem of the risk management of complex or exotic options in the presence of real market imperfections such as transaction costs. The advantages and disadvantages of the various approaches which have appeared in the literature are discussed including a new approach which we are developing.
Motivated by the papers of Dupire (1992) and Derman and Kani (1997), we want to investigate the n... more Motivated by the papers of Dupire (1992) and Derman and Kani (1997), we want to investigate the number of shocks that move the whole implied volatility surface, their interpretation and their correlation with percentage changes in the underlying asset. This work differs from Skiadopoulos, Hodges and Clewlow (1998) in which they looked at the dynamics of smiles for a given maturity bucket. We look at daily changes in implied volatilities under two different metrics: the strike metric and the moneyness metric. Since we are dealing with a three dimensional problem, we fix ranges of days to maturity, we pool them together and we apply the Principal Components Analysis (PCA) to the changes in implied volatilities over time across both the strike (moneyness) metric and the pooled ranges of days to maturity. We find similar results for both metrics. Two shocks explain the movements of the volatility surface, the first shock being interpreted as a shift, while the second one has a Z-shape. The sign of the correlation of the first shock with percentage changes in the underlying asset depends on the metric that we look at, while the sign is positive under both metrics regarding the second shock. The results suggest that the number of shocks, their interpretation and the sign of their correlation with changes in the underlying asset is the same for the whole implied volatility surface as it is for the smile corresponding to a fixed maturity bucket.
In this paper, we develop a general framework for the modelling of Australian electricity market ... more In this paper, we develop a general framework for the modelling of Australian electricity market risk based on the structural relationships in the market. The model framework is designed to be consistent with temperature and load mean forecasts, market forward price quotes, the dependence of load on temperature, and the dependence of price on load. The primary use of the model is for the accurate evaluation of the market risk of an electricity generation and retail company but it can also be used for the valuation of electricity market derivatives and assets. We demonstrate the application of our framework to the Australian National Electricity Market (NEM).
This empirical study is motivated by the models of Dupire (1992) and Derman and Kani (1997). We i... more This empirical study is motivated by the models of Dupire (1992) and Derman and Kani (1997). We investigate the number and shape of shocks that move implied volatility smiles and subsequently we look at the correlation of changes in volatility with changes in the underlying asset. We achieve this by applying Principal Components Analysis on the changes in implied volatilities over time, for fixed ranges of days to maturity and in two different metrics: the strike and the moneyness metric. In contrast to earlier papers in the interest rate literature, we decide on how many principal components explain the implied volatilities dynamics, not by using rules of thumb, but by using Velicer's non-parametric criterion. Subsequently we use a ''Procrustes'' type rotation in order to interpret the retained components. The retained rotated principal components are used for the calculation of the correlation coefficients. We find similar results in both metrics regarding the number and shape of shocks. Two principal components explain the dynamics of smiles. After the rotation the first one is interpreted as shift and the second one has a Z-shape. The correlations for the first principal component depend metric, while for the second are positive under both metrics.
All rights reserved. No part of this work which is copyright may be reproduced or used in any for... more All rights reserved. No part of this work which is copyright may be reproduced or used in any form or by any means-graphic, electronic, or mechanical, including photocopying, recording, taping or information storage and retrieval systems-without the written permission of the ...
Abstract For many interest rate exotic options, for example options on the slope of the yield cur... more Abstract For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or curvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction
... Consider further the “caplet” t:hat caps the interest rate between times T, and T~. Several a... more ... Consider further the “caplet” t:hat caps the interest rate between times T, and T~. Several authors have shown that an instrument that caps the interest rate at rc between Z, and Z, is equivalent to (1 + rcAT) European put options with exercise price Xc = 1/(1 + rcAZ) and expiration ...
Derivatives markets, particularly the over-the-counter market in complex or exotic options, are c... more Derivatives markets, particularly the over-the-counter market in complex or exotic options, are continuing to expand rapidly on a global scale, However, the availability of information regarding the theory and applications of the numerical techniques required to succeed in these markets is limited. This lack of information is extremely damaging to all kinds of financial institutions and consequently there is enormous demand for a source of sound numerical methods for pricing and hedging. Implementing Derivatives Models answers this demand, providing comprehensive coverage of practical pricing and hedging techniques for complex options. Highly accessible to practitioners seeking the latest methods and uses of models, including The Binomial Method Trinomial Trees and Finite Difference Methods Monte Carlo Simulation Implied Trees and Exotic Options Option Pricing, Hedging and Numerical Techniques for Pricing Interest Rate Derivatives Term Structure Consistent Short Rate Models The Heath, Jarrow and Morton Model Implementing Derivatives Models is also a potent resource for financial academics who need to implement, compare, and empirically estimate the behaviour of various option pricing models.
Graphs and Networks. Multilevel Modeling (Geographical Information Systems Series) Second Edition... more Graphs and Networks. Multilevel Modeling (Geographical Information Systems Series) Second Edition A transport network is typically a network of roads, streets, pipes, aqueducts, power lines, or nearly any structure that permits either vehicular movement or the flow of some ...
We discuss the efficiency of the binomial option pricing model for single and multivariate Americ... more We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.
Page 1. ON THE SIMULATIO CONTINGENT Les Clewlow ... Yet in its basic form Monte Carlo simulation ... more Page 1. ON THE SIMULATIO CONTINGENT Les Clewlow ... Yet in its basic form Monte Carlo simulation is not computationally efficient. The Monte Carlo simulation technique for option valuation was first introduced by Boyle [1977]. ...
... Any remaining errors are our responsibility alone. Page 2. 264 GEORGE SKIADOPOULOS, STEWART H... more ... Any remaining errors are our responsibility alone. Page 2. 264 GEORGE SKIADOPOULOS, STEWART HODGES AND LES CLEWLOW ... Page 4. 266 GEORGE SKIADOPOULOS, STEWARTHODGES AND LES CLEWLOW 2. Principal Components Analysis and Implied Volatilities ...
In this paper we discuss the use of mathematical programming techniques linear, dynamic, and goal... more In this paper we discuss the use of mathematical programming techniques linear, dynamic, and goal programming to the problem of the risk management of derivative securities (also known as contingent claims or options). We focus on the problem of the risk management of complex or exotic options in the presence of real market imperfections such as transaction costs. The advantages and disadvantages of the various approaches which have appeared in the literature are discussed including a new approach which we are developing.
Motivated by the papers of Dupire (1992) and Derman and Kani (1997), we want to investigate the n... more Motivated by the papers of Dupire (1992) and Derman and Kani (1997), we want to investigate the number of shocks that move the whole implied volatility surface, their interpretation and their correlation with percentage changes in the underlying asset. This work differs from Skiadopoulos, Hodges and Clewlow (1998) in which they looked at the dynamics of smiles for a given maturity bucket. We look at daily changes in implied volatilities under two different metrics: the strike metric and the moneyness metric. Since we are dealing with a three dimensional problem, we fix ranges of days to maturity, we pool them together and we apply the Principal Components Analysis (PCA) to the changes in implied volatilities over time across both the strike (moneyness) metric and the pooled ranges of days to maturity. We find similar results for both metrics. Two shocks explain the movements of the volatility surface, the first shock being interpreted as a shift, while the second one has a Z-shape. The sign of the correlation of the first shock with percentage changes in the underlying asset depends on the metric that we look at, while the sign is positive under both metrics regarding the second shock. The results suggest that the number of shocks, their interpretation and the sign of their correlation with changes in the underlying asset is the same for the whole implied volatility surface as it is for the smile corresponding to a fixed maturity bucket.
In this paper, we develop a general framework for the modelling of Australian electricity market ... more In this paper, we develop a general framework for the modelling of Australian electricity market risk based on the structural relationships in the market. The model framework is designed to be consistent with temperature and load mean forecasts, market forward price quotes, the dependence of load on temperature, and the dependence of price on load. The primary use of the model is for the accurate evaluation of the market risk of an electricity generation and retail company but it can also be used for the valuation of electricity market derivatives and assets. We demonstrate the application of our framework to the Australian National Electricity Market (NEM).
This empirical study is motivated by the models of Dupire (1992) and Derman and Kani (1997). We i... more This empirical study is motivated by the models of Dupire (1992) and Derman and Kani (1997). We investigate the number and shape of shocks that move implied volatility smiles and subsequently we look at the correlation of changes in volatility with changes in the underlying asset. We achieve this by applying Principal Components Analysis on the changes in implied volatilities over time, for fixed ranges of days to maturity and in two different metrics: the strike and the moneyness metric. In contrast to earlier papers in the interest rate literature, we decide on how many principal components explain the implied volatilities dynamics, not by using rules of thumb, but by using Velicer's non-parametric criterion. Subsequently we use a ''Procrustes'' type rotation in order to interpret the retained components. The retained rotated principal components are used for the calculation of the correlation coefficients. We find similar results in both metrics regarding the number and shape of shocks. Two principal components explain the dynamics of smiles. After the rotation the first one is interpreted as shift and the second one has a Z-shape. The correlations for the first principal component depend metric, while for the second are positive under both metrics.
All rights reserved. No part of this work which is copyright may be reproduced or used in any for... more All rights reserved. No part of this work which is copyright may be reproduced or used in any form or by any means-graphic, electronic, or mechanical, including photocopying, recording, taping or information storage and retrieval systems-without the written permission of the ...
Abstract For many interest rate exotic options, for example options on the slope of the yield cur... more Abstract For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or curvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction
... Consider further the “caplet” t:hat caps the interest rate between times T, and T~. Several a... more ... Consider further the “caplet” t:hat caps the interest rate between times T, and T~. Several authors have shown that an instrument that caps the interest rate at rc between Z, and Z, is equivalent to (1 + rcAT) European put options with exercise price Xc = 1/(1 + rcAZ) and expiration ...
Derivatives markets, particularly the over-the-counter market in complex or exotic options, are c... more Derivatives markets, particularly the over-the-counter market in complex or exotic options, are continuing to expand rapidly on a global scale, However, the availability of information regarding the theory and applications of the numerical techniques required to succeed in these markets is limited. This lack of information is extremely damaging to all kinds of financial institutions and consequently there is enormous demand for a source of sound numerical methods for pricing and hedging. Implementing Derivatives Models answers this demand, providing comprehensive coverage of practical pricing and hedging techniques for complex options. Highly accessible to practitioners seeking the latest methods and uses of models, including The Binomial Method Trinomial Trees and Finite Difference Methods Monte Carlo Simulation Implied Trees and Exotic Options Option Pricing, Hedging and Numerical Techniques for Pricing Interest Rate Derivatives Term Structure Consistent Short Rate Models The Heath, Jarrow and Morton Model Implementing Derivatives Models is also a potent resource for financial academics who need to implement, compare, and empirically estimate the behaviour of various option pricing models.
Graphs and Networks. Multilevel Modeling (Geographical Information Systems Series) Second Edition... more Graphs and Networks. Multilevel Modeling (Geographical Information Systems Series) Second Edition A transport network is typically a network of roads, streets, pipes, aqueducts, power lines, or nearly any structure that permits either vehicular movement or the flow of some ...
We discuss the efficiency of the binomial option pricing model for single and multivariate Americ... more We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.
Page 1. ON THE SIMULATIO CONTINGENT Les Clewlow ... Yet in its basic form Monte Carlo simulation ... more Page 1. ON THE SIMULATIO CONTINGENT Les Clewlow ... Yet in its basic form Monte Carlo simulation is not computationally efficient. The Monte Carlo simulation technique for option valuation was first introduced by Boyle [1977]. ...
... Any remaining errors are our responsibility alone. Page 2. 264 GEORGE SKIADOPOULOS, STEWART H... more ... Any remaining errors are our responsibility alone. Page 2. 264 GEORGE SKIADOPOULOS, STEWART HODGES AND LES CLEWLOW ... Page 4. 266 GEORGE SKIADOPOULOS, STEWARTHODGES AND LES CLEWLOW 2. Principal Components Analysis and Implied Volatilities ...
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