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A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models

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  • René Garcia
  • Èric Renault

Abstract

Recently, Duan (1995) proposed a GARCH option pricing formula and a corresponding hedging formula. In a similar ARCH-type model for the underlying asset, Kallsen and Taqqu (1994) arrived at a hedging formula different from Duan's although they concur on the pricing formula. In this note, we explain this difference by pointing out that the formula developed by Kallsen and Taqqu corresponds to the usual concept of hedging in the context of ARCH-type models. We argue, however, that Duan's formula has some appeal and we propose a stochastic volatility model that ensures its validity. We conclude by a comparison of ARCH-type and stochastic volatility option pricing models. Copyright Blackwell Publishers 1998.

Suggested Citation

  • René Garcia & Èric Renault, 1998. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 153-161.
  • Handle: RePEc:bla:mathfi:v:8:y:1998:i:2:p:153-161
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    References listed on IDEAS

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    1. Marcel Boyer, 1997. "Competition and Access in Telecoms: ECPR, Global Price Cap, and Auctions," CIRANO Working Papers 97s-03, CIRANO.
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    Cited by:

    1. Montmarquette, Claude & Cannings, Kathy & Mahseredjian, Sophie, 2002. "How do young people choose college majors?," Economics of Education Review, Elsevier, pages 543-556.
    2. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers 2002s-33, CIRANO.
    3. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, pages 1204-1221.
    4. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
    5. René Garcia & Eric Renault, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Working Papers 98-10, Center for Research in Economics and Statistics.
    6. René Garcia & Éric Renault, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," CIRANO Working Papers 98s-02, CIRANO.
    7. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, pages 321-342.
    8. Bruno R'emillard & Sylvain Rubenthaler, 2012. "Optimal hedging in discrete time," Papers 1211.5035, arXiv.org.
    9. Garcia, R. & Renault, E., 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, pages 321-342.
    11. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, pages 242-261.
    12. Jin-Chuan Duan & Peter H. Ritchken & Zhiqiang Sun, 2006. "Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities," Working Paper 0619, Federal Reserve Bank of Cleveland.

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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets

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