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Short-term options with stochastic volatility: Estimation and empirical performance

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  • Gabriele Fiorentini
  • Angel León
  • Gonzalo Rubio

Abstract

This paper examines the stochastic volatility model suggested by Heston (1993). We employ a time-series approach to estimate the model and we discuss the potential effects of time-varying skewness and kurtosis on the performance of the model. In particular, it is found that the model tends to overprice out-of-the-money calls and underprice in-the-money calls. It is also found that the daily volatility risk premium presents a quite volatile behavior over time; however, our evidence suggests that the volatility risk premium has a negligible impact on the pricing performance of Heston´s model.

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Paper provided by FEDEA in its series Studies on the Spanish Economy with number 02.

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Handle: RePEc:fda:fdaeee:02

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  1. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  2. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
  3. Guo, Dajiang, 1998. "The Risk Premium of Volatility Implicit in Currency Options," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 498-507, October.
  4. Jens Carsten Jackwerth., 1996. "Implied Binomial Trees: Generalizations and Empirical Tests," Research Program in Finance Working Papers RPF-262, University of California at Berkeley.
  5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
  6. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 211-239, June.
  7. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
  8. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
  9. 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.
  10. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  12. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
  13. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  14. Angel León & Juan Mora, 1999. "Modelling conditional heteroskedasticity: Application to the "IBEX-35" stock-return index," Spanish Economic Review, Springer, vol. 1(3), pages 215-238.
  15. 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.
  16. 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.
  17. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  18. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  19. 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.
  20. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
  21. Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
  22. Mikhail Chernov & Eric Ghysels, 1998. "What Data Should Be Used to Price Options?," CIRANO Working Papers 98s-22, CIRANO.
  23. French, Dan W., 1984. "The weekend effect on the distribution of stock prices : Implications for option pricing," Journal of Financial Economics, Elsevier, vol. 13(4), pages 547-559, December.
  24. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
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Cited by:
  1. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2004. "Nonparametric Estimation of Convergence of Interest Rates: Effects on Bond Pricing," Faculty Working Papers 03/04, School of Economics and Business Administration, University of Navarra.
  2. Pilar Corredor-Casado & Rafael Santamaría-Aquilué, 2000. "La estructura temporal de las volatilidades implícitas en la opción sobre el IBEX-35," Investigaciones Economicas, Fundación SEPI, vol. 24(2), pages 385-417, May.

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