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Hedging of time discrete auto-regressive stochastic volatility options

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  • Joan del Castillo
  • Juan-Pablo Ortega
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    Abstract

    Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a non-trivial exercise due to the incomplete nature of the corresponding market. In this paper we apply two volatility estimation techniques available in the literature for these models, namely Kalman filtering and the hierarchical-likelihood approach, in order to implement various pricing and dynamical hedging strategies. Our study shows that the local risk minimization scheme developed by F\"ollmer, Schweizer, and Sondermann is particularly appropriate in this setup, especially for at and in the money options or for low hedging frequencies.

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    Paper provided by arXiv.org in its series Papers with number 1110.6322.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.6322

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    1. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Documents de travail du Centre d'Economie de la Sorbonne 10023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Glen, Andrew G. & Leemis, Lawrence M. & Drew, John H., 2004. "Computing the distribution of the product of two continuous random variables," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 451-464, January.
    3. Torben G. Andersen & Hyung-Jin Chung & Bent E. Sorensen, . "EMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Computing in Economics and Finance 1997 6, Society for Computational Economics.
    4. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 319-342.
    7. Sanae Tashiro & Chu-Ping Lo, 2011. "Balancing nutrition, luxury, and time constraints in food preparation choices," China Agricultural Economic Review, Emerald Group Publishing, vol. 3(2), pages 245-265, May.
    8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
    9. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    10. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185.
    11. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
    12. Jin-Chuan Duan & Geneviève Gauthier & Jean-Guy Simonato, 2001. "Asymptotic Distribution of the EMS Option Price Estimator," Management Science, INFORMS, vol. 47(8), pages 1122-1132, August.
    13. Robert J. Elliott & Dilip B. Madan, 1998. "A Discrete Time Equivalent Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 127-152.
    14. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    15. Lee, Woojoo & Lim, Johan & Lee, Youngjo & del Castillo, Joan, 2011. "The hierarchical-likelihood approach to autoregressive stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 248-260, January.
    16. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    17. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
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