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Pricing Stock Options under Stochastic Volatility and Stochastic Interest Rates with Efficient Method of Moments Estimation

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  • George J. Jiang

    ()
    (University of Groningen)

  • Pieter J. van der Sluis

    ()
    (University of Amsterdam)

Abstract

While the stochastic volatility (SV) generalization has been shown to improvethe explanatory power compared to the Black-Scholes model, the empiricalimplications of the SV models on option pricing have not been adequately tested.The purpose of this paper is to first estimate a multivariate SV model using theefficient method of moments (EMM) technique and then investigate the respectiveeffect of stochastic interest rate, systematic volatility and idiosyncraticvolatility on option prices. We compute option prices using both underlyinghistorical volatilities obtained through reprojection and volatilities impliedfrom observed option prices and gauge each model's performance through directcomparison with observed market option prices. Our results suggest: (i) Whiletheory predicts that the short-term interest rates are strongly related to thesystematc volatility of the consumption process, our estimation results suggestthat the short-term interest rate fails to be a good proxy of the systematicfactor; (ii) While allowing for stochastic volatility of stock returns can ingeneral reduce the pricing errors and allowing for asymmetry or "leverageeffect'' in the SV models does help to explain the skewness of the volatility"smile'', allowing for stochastic interest rate has minimal impact on optionprices in our case; (iii) Similar to Melino and Turnbull (1990), our empiricalfindings strongly suggest the existence of a non-zero risk premum for stochasticvolatility of stock returns. Allowing for non-zero risk-premium of stochasticvolatility and based on implied volatility, the SV models can largely reduce theoption pricing errors, suggesting the importance of incorporating theinformation in the options market in pricing options.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 98-067/4.

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Date of creation: 04 Jun 1998
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Handle: RePEc:dgr:uvatin:19980067

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References

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Cited by:
  1. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
  2. In Kim & In-Seok Baek & Jaesun Noh & Sol Kim, 2007. "The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics," Review of Quantitative Finance and Accounting, Springer, vol. 29(1), pages 69-110, July.
  3. Paola Zerilli, 2007. "Option Pricing and Spikes in Volatility: Theoretical and Empirical Analysis," Discussion Papers 07/08, Department of Economics, University of York.
  4. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.

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