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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

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

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Web page: http://www.elsevier.com/locate/jempfin

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  1. 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.
  2. HARDLE, Wolfgang & HAFNER, Christian M., . "Discrete time option pricing with flexible volatility estimation," CORE Discussion Papers RP -1439, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  6. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
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  8. Christian M. Hafner & Helmut Herwartz, 2000. "Testing for linear autoregressive dynamics under heteroskedasticity," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 177-197.
  9. 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.
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  12. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
  13. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
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Cited by:
  1. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Bauwens, L. & Lubrano, M., 2000. "Bayesian Option Pricing using Asymmetric Garch Models," G.R.E.Q.A.M. 00a18, Universite Aix-Marseille III.
  3. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
  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., vol. 20(3), pages 377-404.
  5. 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.
  6. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 540-582, Fall.
  7. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, vol. 223(1), pages 188-202.
  8. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
  9. 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, vol. 16(3), pages 291-314, July.
  10. 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 0116, Faculty of Economics, University of Cambridge.

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