A GARCH Option Pricing Model with Filtered Historical Simulation

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

[1]  J. D. da Fonseca,et al.  Riding on the smiles , 2010 .

[2]  Peter Carr,et al.  Variance Risk Premiums , 2009 .

[3]  Luca Benzoni,et al.  Stochastic Volatility , 2008, Encyclopedia of Complexity and Systems Science.

[4]  Peter F. Christoffersen,et al.  Option Valuation with Long-Run and Short-Run Volatility Components , 2008 .

[5]  Liuren Wu,et al.  Variance Risk Dynamics, Variance Risk Premia, and Optimal Variance Swap Investments , 2007 .

[6]  P. Carr,et al.  Variance Risk Premia , 2007 .

[7]  W. Härdle,et al.  Empirical Pricing Kernels and Investor Preferences , 2007 .

[8]  R. Elliott,et al.  Cutting the hedge , 2007 .

[9]  Stylianos Perrakis,et al.  Mispricing of S&P 500 Index Options , 2006 .

[10]  Peter F. Christoffersen,et al.  Option Valuation with Conditional Skewness , 2003 .

[11]  M. Yor,et al.  Stochastic Volatility for Lévy Processes , 2003 .

[12]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[13]  J. Jackwerth,et al.  The Price of a Smile: Hedging and Spanning in Option Markets , 2001 .

[14]  S. Heston,et al.  A Closed-Form GARCH Option Valuation Model , 2000 .

[15]  E. Ghysels,et al.  A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation , 2000 .

[16]  A. Lo,et al.  Nonparametric Risk Management and Implied Risk Aversion , 2000 .

[17]  R. Engle,et al.  Empirical Pricing Kernels , 1999 .

[18]  J. Jackwerth.  Recovering Risk Aversion from Option Prices and Realized Returns , 1998 .

[19]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[20]  P. Glasserman,et al.  Monte Carlo methods for security pricing , 1997 .

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

[22]  Guojun Wu,et al.  Asymmetric Volatility and Risk in Equity Markets , 1997 .

[23]  Kaushik I. Amin,et al.  Inferring Future Volatility from the Information in Implied Volatility in Eurodollar Options: A New Approach , 1997 .

[24]  A. Lo,et al.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1996, Macroeconomic Dynamics.

[25]  M. Stutzer.  A Simple Nonparametric Approach to Derivative Security Valuation , 1996 .

[26]  Jeff Fleming,et al.  Implied volatility functions: empirical tests , 1996, IEEE/IAFE 1996 Conference on Computational Intelligence for Financial Engineering (CIFEr).

[27]  Robert A. Jarrow,et al.  OPTION PRICING USING THE TERM STRUCTURE OF INTEREST RATES TO HEDGE SYSTEMATIC DISCONTINUITIES IN ASSET RETURNS1 , 1995 .

[28]  M. Rubinstein..  Implied Binomial Trees , 1994 .

[29]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[30]  S. Heston.  Invisible Parameters in Option Prices , 1993 .

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

[32]  Wayne E. Ferson,et al.  Seasonality and Consumption-Based Asset Pricing , 1992 .

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

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

[35]  R. Engle,et al.  Semiparametric ARCH Models , 1991 .

[36]  J. Campbell,et al.  No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns , 1991 .

[37]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[38]  Ravi Jagannathan,et al.  Implications of Security Market Data for Models of Dynamic Economies , 1990, Journal of Political Economy.

[39]  Lars Peter Hansen,et al.  THE ROLE OF CONDITIONING INFORMATION IN DEDUCING TESTABLE RESTRICTIONS IMPLIED BY DYNAMIC ASSET PRICING MODELS1 , 1987 .

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

[41]  David P. Brown,et al.  A Simple Econometric Approach for Utility‐Based Asset Pricing Models , 1985 .

[42]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[43]  L. Hansen,et al.  Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns , 1983, Journal of Political Economy.

[44]  A. Christie,et al.  The stochastic behavior of common stock variances: value , 1982 .

[45]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[46]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[47]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[48]  Michael J. Brennan,et al.  The Pricing of Contingent Claims in Discrete Time Models , 1979 .

[49]  R. Lucas.  ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[50]  M. Rubinstein..  THE STRONG CASE FOR THE GENERALIZED LOGARITHMIC UTILITY MODEL AS THE PREMIER MODEL OF FINANCIAL MARKETS , 1976 .

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

[52]  K. Arrow.  The Role of Securities in the Optimal Allocation of Risk-bearing , 1964 .

[53]  J. Geanakoplos,et al.  Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models , 2007 .

[54]  R. Engle.  Arch Models " , 1999 .

[55]  D. Slesnick.  Are Our Data Relevant to the Theory? The Case of Aggregate Consumption , 1998 .

[56]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[57]  N. Shephard.  Statistical aspects of ARCH and stochastic volatility , 1996 .

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

[59]  Bruno Dupire.  Pricing with a Smile , 1994 .

[60]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[61]  David W. Wilcox.  The Construction of U.S. Consumption Data: Some Facts and Their Implications for Empirical Work , 1992 .

[62]  J. Wooldridge,et al.  Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances , 1992 .

[63]  C. L. Sheng.  A Theory of Value , 1991 .

[64]  S. Ross.  A Simple Approach to the Valuation of Risky Streams , 1978 .

[65]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

[66]  Mark Rubinstein,et al.  The Valuation of Uncertain Income Streams and the Pricing of Options , 1976 .

[67]  H. Uzawa,et al.  Optimal Growth in a Two-Sector Model of Capital Accumulation , 1964 .

[68]  G. Debreu,et al.  Theory of Value , 1959 .

[69]  J. Duan,et al.  Série Scientifique Scientific Series Empirical Martingale Simulation for Asset Prices Empirical Martingale Simulation for Asset Prices , 2022 .