INDEX OPTION PRICING MODELS WITH

INDEX OPTION PRICING MODELS WITH - Center for Economic...

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Center for Economic Research No. 2000-36 INDEX OPTION PRICING MODELS WITH STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES By George J. Jiang and Pieter J. van der Sluis March 2000 ISSN 0924-7815
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Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates George J. Jiang Schulich School of Business York University Pieter J. van der Sluis Department of Econometrics/CentER Tilburg University March 13, 2000 George J. Jiang, Finance Area, Schulich School of Business, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3. Tel: (416) 736-2100 ext. 33302, (416) 736-5073 and Fax: (416) 736-5687. E-mail: [email protected] George J. Jiang is also a SOM research fellow of the Faculty of Business and Economics at the University of Groningen in The Netherlands. Pieter J. van der Sluis, Department of Econometrics/CentER, Tilburg University, P.O. Box 90153, NL-5000 LE Tilburg, The Netherlands, phone +31 13 466 2911, fax +31 13 466 3280, email: [email protected]
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Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates Abstract: This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model’s performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or “leverage effect” does help to explain the skewness of the volatility “smile”, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino & Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficient in modeling short-term kurtosis of asset returns, an SV model with fatter-tailed noise or jump component may have better explanatory power. Keywords: Stochastic Volatility, Efficient Method of Moments (EMM), Reprojection, Option Pricing.
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INDEX OPTION PRICING MODELS WITH - Center for Economic...

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