GARCH vs. stochastic volatility: Option pricing and risk management

This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the fit to observed prices, GARCH clearly dominates both stochastic volatility and the benchmark Black Scholes model. However, the predictions of the market risk from hypothetical derivative positions show sizable errors. The fit to the realized profits and losses is poor and there are no notable differences between the models. Overall we therefore observe that the more complex option pricing models can improve on the Black Scholes methodology only for the purpose of pricing, but not for the Value-at-Risk forecasts. (author's abstract)

[1]  Paul H. Kupiec,et al.  Techniques for Verifying the Accuracy of Risk Measurement Models , 1995 .

[2]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[3]  Rajna Gibson,et al.  Model risk : concepts, calibration and pricing , 2000 .

[4]  Saikat Nandi,et al.  Options and volatility , 1996 .

[5]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[6]  Peter J.G. Vlaar.  Value at risk models for Dutch bond portfolios , 2000 .

[7]  William H. Press,et al.  Numerical recipes in C , 2002 .

[8]  David S. Bates.  Testing Option Pricing Models , 1995 .

[9]  Gurdip Bakshi,et al.  Pricing and hedging long-term options , 2000 .

[10]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[11]  Philippe Jorion.  Value at risk: the new benchmark for controlling market risk , 1996 .

[12]  J. Duan.  THE GARCH OPTION PRICING MODEL , 1995 .

[13]  Phelim P. Boyle,et al.  Advances in Futures and Options Research , 1996 .

[14]  Stefan Pichler,et al.  A comparison of analytical VaR methodologies for portfolios that include options , 1999 .

[15]  Jin-Chuan Duan.  A Unified Theory of Option Pricing under Stochastic Volatility from GARCH to Diffusion , 1994 .

[16]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[17]  R. Engle,et al.  Implied ARCH models from options prices , 1992 .

[18]  Jin-Chuan Duan,et al.  Pricing Hang Seng Index options around the Asian financial crisis – A GARCH approach , 2001 .

[19]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[20]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[21]  J. Hull.  Options, Futures, and Other Derivatives , 1989 .

[22]  Jose A. Lopez.  Regulatory evaluation of value-at-risk models , 1998 .

[23]  Saikat Nandi,et al.  How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market , 1998 .

[24]  Christopher G. Lamoureux,et al.  Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities , 1993 .

[25]  Jeremy Berkowitz.  Evaluating the Forecasts of Risk Models , 1999 .

[26]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[27]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[28]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[29]  Jinyong Hahn,et al.  Série Scientifique Scientific Series Testing and Comparing Value-at-risk Measures , 2022 .

[30]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[31]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[32]  M. Pritsker.  Evaluating Value at Risk Methodologies: Accuracy versus Computational Time , 1996 .