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Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model

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  • Massimo Caccia
  • Bruno R'emillard

Abstract

In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial time series and our model covers both. To illustrate the relevance of our proposed methodology, we first compare the proposed model with the well-known hidden Markov model via likelihood ratio tests and a novel goodness-of-fit test on the S\&P 500 daily returns. Secondly, we present out-of-sample hedging results on S\&P 500 vanilla options as well as a trading strategy based on theoretical prices, which we compare to simpler models including the classical Black-Scholes delta-hedging approach.

Suggested Citation

  • Massimo Caccia & Bruno R'emillard, 2017. "Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model," Papers 1707.02019, arXiv.org.
    • Handle: RePEc:arx:papers:1707.02019
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    3. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. 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 637-654, May-June.
    6. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    7. Jeff Fleming & Chris Kirby & Barbara Ostdiek, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
    8. Hamilton, James D & Gang, Lin, 1996. "Stock Market Volatility and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 573-593, Sept.-Oct.
    9. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    10. Buraschi, Andrea & Jackwerth, Jens, 2001. "The Price of a Smile: Hedging and Spanning in Option Markets," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 495-527.
    11. 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.
    12. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    13. Ping Wu & Robert J. Elliott, 2005. "Parameter Estimation For A Regime-Switching Mean-Reverting Model With Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 791-806.
    14. repec:bla:jfinan:v:44:y:1989:i:5:p:1115-53 is not listed on IDEAS
    15. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    16. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    17. Bruno R�millard & Sylvain Rubenthaler, 2013. "Optimal hedging in discrete time," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 819-825, May.
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