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Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

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Author Info

  • Jiang, G.J.
  • Sluis, P.J. van der

    (Tilburg University, Center for Economic Research)

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 inpricing 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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2000-36.

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Date of creation: 2000
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Handle: RePEc:dgr:kubcen:200036

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Related research

Keywords: Stochastic Volatility; Efficient Method of Moments (EMM); Reprojection; Option Pricing;

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References

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Citations

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Cited by:
  1. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06.
  2. Carmen Broto & Esther Ruiz, 2002. "Estimation Methods For Stochastic Volatility Models: A Survey," Statistics and Econometrics Working Papers ws025414, Universidad Carlos III, Departamento de Estadística y Econometría.
  3. PREMINGER, Arie & HAFNER, Christian M., 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Juho Kanniainen & Robert Pich\'e, 2012. "Stock Price Dynamics and Option Valuations under Volatility Feedback Effect," Papers 1209.4718, arXiv.org.
  5. Anna Pajor, 2009. "A Note on Option Pricing with the Use of Discrete-Time Stochastic Volatility Processes," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(1), pages 71-81, March.

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