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Option pricing and hedging under a stochastic volatility Lévy process model

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Abstract

In this paper, we discuss a stochastic volatility model with a Lévy driving process and then apply the model to option pricing and hedging. The stochastic volatility in our model is defined by the continuous Markov chain. The risk-neutral measure is obtained by applying the Esscher transform. The option price using this model is computed by the Fourier transform method. We obtain the closed-form solution for the hedge ratio by applying locally risk-minimizing hedging.

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Authors and Affiliations

  1. Department of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Young Shin Kim & Svetlozar T. Rachev

  2. EDHEC Business School, New York, NY, USA

    Frank J. Fabozzi

  3. HECTOR School of Engineering and Management, International Department, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Zuodong Lin

  4. Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA

    Svetlozar T. Rachev

  5. FinAnalytica, Seattle, WA, Germany

    Svetlozar T. Rachev

Authors
  1. Young Shin Kim
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  2. Frank J. Fabozzi
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  3. Zuodong Lin
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  4. Svetlozar T. Rachev
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Corresponding author

Correspondence to Frank J. Fabozzi.

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Kim, Y.S., Fabozzi, F.J., Lin, Z. et al. Option pricing and hedging under a stochastic volatility Lévy process model. Rev Deriv Res 15, 81–97 (2012). https://doi.org/10.1007/s11147-011-9070-9

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  • DOI: https://doi.org/10.1007/s11147-011-9070-9

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