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Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis

  • Hafner, Christian M.
  • Herwartz, Helmut

Daily returns of financial assets are frequently found to exhibit positive autocorrelation at lag 1. When specifying a linear AR(l) conditional mean, one may ask how this predictability affects option prices. We investigate the dependence of option prices on autoregressive dynamics under stylized facts of stock returns, i.e., conditional heteroskedasticity: leverage effect, and conditional leptokurtosis. Our analysis covers both a continuous and discrete time framework. The results suggest that a non-zero autoregression coefficient tends to increase the deviation of option prices from Black & Scholes prices caused by stochastic volatility.

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Article provided by Elsevier in its journal Journal of Empirical Finance.

Volume (Year): 8 (2001)
Issue (Month): 1 (March)
Pages: 1-34

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Handle: RePEc:eee:empfin:v:8:y:2001:i:1:p:1-34
Contact details of provider: Web page: http://www.elsevier.com/locate/jempfin

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  1. Andrew W. Lo & Jiang Wang, 1994. "Implementing Option Pricing Models When Asset Returns Are Predictable," NBER Working Papers 4720, National Bureau of Economic Research, Inc.
  2. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  4. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. Christian M. Hafner & Wolfgang HÄrdle, 2000. "Discrete time option pricing with flexible volatility estimation," Finance and Stochastics, Springer, vol. 4(2), pages 189-207.
  7. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap : Continuous time GARCH modeling," Other publications TiSEM c3d29817-403a-4ad1-9295-8, Tilburg University, School of Economics and Management.
  8. Hafner, Christian M. & Herwartz, Helmut, 1998. "Testing for linear autoregressive dynamics under heteroskedasticity," SFB 373 Discussion Papers 1999,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  9. 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.
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  11. H. Herwartz, 1998. "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," SFB 373 Discussion Papers 1998,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  13. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
  14. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  15. Drost, F.C. & Werker, B.J.M., 1994. "Closing the GARCH gap : Continuous time GARCH modeling," Discussion Paper 1994-2, Tilburg University, Center for Economic Research.
  16. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  17. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  18. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
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