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

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  • Hafner, Christian M.
  • Herwartz, Helmut

Abstract

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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Bibliographic Info

Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1999,58.

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Date of creation: 1999
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Handle: RePEc:zbw:sfb373:199958

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Keywords: option pricing; autoregression; heteroskedasticity; GARCH; leverage effect; conditional leptokurtosis;

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References

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  1. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  2. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(1), pages 13-32.
  3. 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.
  4. Lo, Andrew W. (Andrew Wen-Chuan) & Wang, Jiang, 1959-, 1993. "Implementing option pricing models when asset returns are predictable," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 3593-93., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  5. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 31-57, September.
  6. Härdle, Wolfgang & Hafner, Christian M., 1997. "Discrete time option pricing with flexible volatility estimation," SFB 373 Discussion Papers 1997,56, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  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. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers, Tilburg - Center for Economic Research 9240, Tilburg - Center for Economic Research.
  10. 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, Econometric Society, vol. 55(2), pages 391-407, March.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. 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, University of Chicago Press, vol. 96(1), pages 116-31, February.
  13. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
  14. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  15. repec:wop:humbsf:1999-7 is not listed on IDEAS
  16. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B, University of Bonn, Germany 209, University of Bonn, Germany.
  17. repec:wop:humbsf:1998-41 is not listed on IDEAS
  18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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Citations

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Cited by:
  1. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Forecasting of Options Prices: A Natural Framework for Pooling Historical and Implied Volatiltiy Information," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0116, Faculty of Economics, University of Cambridge.
  2. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 13(1), pages 113-128, January.
  3. Hafner, C.M., 2003. "Simple approximations for option pricing under mean reversion and stochastic volatility," Econometric Institute Research Papers EI 2003-20, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  4. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(3), pages 377-404.
  5. Bauwens, L. & Lubrano, M., 2000. "Bayesian Option Pricing using Asymmetric Garch Models," G.R.E.Q.A.M., Universite Aix-Marseille III 00a18, Universite Aix-Marseille III.
  6. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
  7. Lim, G.C. & Martin, G.M. & Martin, V.L., 2006. "Pricing currency options in the presence of time-varying volatility and non-normalities," Journal of Multinational Financial Management, Elsevier, Elsevier, vol. 16(3), pages 291-314, July.
  8. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, Elsevier, vol. 223(1), pages 188-202.
  9. Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, School of Economics and Management, University of Aarhus.
  10. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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