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An Empirical Comparison of Two Stochastic Volatility Models using Indian Market Data

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  • Srikanth Iyer

    ()

  • Seema Nanda

    ()

  • Swapnil Kumar
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    Abstract

    We conduct an empirical comparison of hedging strategies for two different stochastic volatility models proposed in the literature. One is an asymptotic expansion approach and the other is the risk-minimizing approach applied to a Markov-switched geometric Brownian motion. We also compare these with the Black–Scholes delta hedging strategies using historical and implied volatilities. The derivatives we consider are European call options on the NIFTY index of the Indian National Stock Exchange. We compare a few cases with profit and loss data from a trading desk. We find that for the cases that we analyzed, by far the better results are obtained for the Markov-switched geometric Brownian motion. Copyright Springer Science+Business Media New York 2013

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    File URL: http://hdl.handle.net/10.1007/s10690-013-9166-3
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    Bibliographic Info

    Article provided by Springer in its journal Asia-Pacific Financial Markets.

    Volume (Year): 20 (2013)
    Issue (Month): 3 (September)
    Pages: 243-259

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    Handle: RePEc:kap:apfinm:v:20:y:2013:i:3:p:243-259

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    Web page: http://springerlink.metapress.com/link.asp?id=102851

    Related research

    Keywords: Option pricing; Stochastic volatility; Mean reverting; Regime switching; Risk minimizing; C02; C90; G13;

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    1. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    3. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Rolf Poulsen & Klaus Reiner Schenk-Hoppe & Christian-Oliver Ewald, 2009. "Risk minimization in stochastic volatility models: model risk and empirical performance," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 693-704.
    5. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    7. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.
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