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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

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

Suggested Citation

  • Srikanth Iyer & Seema Nanda & Swapnil Kumar, 2013. "An Empirical Comparison of Two Stochastic Volatility Models using Indian Market Data," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(3), pages 243-259, September.
    • Handle: RePEc:kap:apfinm:v:20:y:2013:i:3:p:243-259
    DOI: 10.1007/s10690-013-9166-3
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    References listed on IDEAS

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    1. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.
    2. 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.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    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.
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    More about this item

    Keywords

    Option pricing; Stochastic volatility; Mean reverting; Regime switching; Risk minimizing; C02; C90; G13;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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