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

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Author Info
George J. Jiang () (University of Groningen)
Pieter J. van der Sluis () (University of Amsterdam)

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Abstract

While the stochastic volatility (SV) generalization has been shown to improve the explanatory power compared to the Black-Scholes model, the empirical implications 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 the efficient method of moments (EMM) technique and then investigate the respective effect of stochastic interest rate, systematic volatility and idiosyncratic volatility on option prices. We compute option prices using both underlying historical volatilities obtained through reprojection and volatilities implied from observed option prices and gauge each model's performance through direct comparison with observed market option prices. Our results suggest: (i) While theory predicts that the short-term interest rates are strongly related to the systematc volatility of the consumption process, our estimation results suggest that the short-term interest rate fails to be a good proxy of the systematic factor; (ii) While allowing for stochastic volatility of stock returns can in general reduce the pricing errors and allowing for asymmetry or "leverage effect'' in the SV models does help to explain the skewness of the volatility "smile'', allowing for stochastic interest rate has minimal impact on option prices in our case; (iii) Similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premum for stochastic volatility of stock returns. Allowing for non-zero risk-premium of stochastic volatility and based on implied volatility, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information in the options market in pricing options.

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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 listed on IDEAS
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  1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(4), pages 727-52. [Downloadable!] (restricted)
  2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  3. Fenton, Victor M & Gallant, A Ronald, 1996. "Convergence Rates of SNP Density Estimators," Econometrica, Econometric Society, vol. 64(3), pages 719-27, May. [Downloadable!] (restricted)
  4. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265. [Downloadable!] (restricted)
  5. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April. [Downloadable!] (restricted)
  6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  7. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De. [Downloadable!] (restricted)
  8. Ronald Mahieu & Peter Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis. [Downloadable!]
  9. Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers 96-17, Duke University, Department of Economics.
  10. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(4), pages 427-445. [Downloadable!] (restricted)
  11. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July. [Downloadable!] (restricted)
  12. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 493-521. [Downloadable!] (restricted)
  13. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De. [Downloadable!] (restricted)
    Other versions:
  14. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  15. Bansal, Ravi & Gallant, A. Ronald & Hussey, Robert & Tauchen, George, 1995. "Nonparametric estimation of structural models for high-frequency currency market data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 251-287. [Downloadable!] (restricted)
  16. Bailey, Warren & Stulz, Ren? M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(01), pages 1-12, March. [Downloadable!]
  17. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January. [Downloadable!] (restricted)
    Other versions:
  18. Pieter J. van der Sluis, 1997. "Post-Sample Prediction Tests for the Efficient Method of Moments," Tinbergen Institute Discussion Papers 97-054/4, Tinbergen Institute. [Downloadable!]
  19. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(02), pages 143-151, June. [Downloadable!]
  20. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-52, July.
    Other versions:
  21. Jones, E. Philip, 1984. "Option arbitrage and strategy with large price changes," Journal of Financial Economics, Elsevier, vol. 13(1), pages 91-113, March. [Downloadable!] (restricted)
  22. Pieter J. van der Sluis, 1997. "Computationally Attractive Stability Tests for the Efficient Method of Moments," Tinbergen Institute Discussion Papers 97-087/4, Tinbergen Institute. [Downloadable!]
    Other versions:
  23. Bates, David S, 1991. " The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-44, July. [Downloadable!] (restricted)
  24. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  25. Karolyi, G. Andrew, 1993. "A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 579-594, December. [Downloadable!]
  26. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  27. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September. [Downloadable!] (restricted)
  28. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May. [Downloadable!] (restricted)
  29. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  30. G Sandmann & Siem Jan Koopman, 1996. "Maximum Likelihood Estimation of Stochastic Volatility Models," FMG Discussion Papers dp248, Financial Markets Group. [Downloadable!] (restricted)
  31. Jón Daníelsson, 1996. "Estimation of the Stochastic Volatility Models by Simulated Maximum Likelihood: C++ Code," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 1(1). [Downloadable!]
  32. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December. [Downloadable!] (restricted)
  33. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management. [Downloadable!]
  34. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
  35. Xu, Xinzhong & Taylor, Stephen J., 1994. "The Term Structure of Volatility Implied by Foreign Exchange Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 57-74, March. [Downloadable!]
  36. Ruiz, Esther, 1994. "Quasi-maximum likelihood estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 63(1), pages 289-306, July. [Downloadable!] (restricted)
  37. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management. [Downloadable!]
  38. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-25, September. [Downloadable!] (restricted)
    Other versions:
  39. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November. [Downloadable!] (restricted)
  40. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
    Other versions:
  41. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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  1. 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. [Downloadable!] (restricted)
  2. Paola Zerilli, 2005. "Option pricing and spikes in volatility: theoretical and empirical analysis," Money Macro and Finance (MMF) Research Group Conference 2005 76, Money Macro and Finance Research Group. [Downloadable!]
  3. Paola Zerilli, 2007. "Option Pricing and Spikes in Volatility: Theoretical and Empirical Analysis," Discussion Papers 07/08, Department of Economics, University of York. [Downloadable!]
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