Review of Derivatives Research

, Volume 15, Issue 1, pp 81–97 | Cite as

Option pricing and hedging under a stochastic volatility Lévy process model

  • Young Shin Kim
  • Frank J. Fabozzi
  • Zuodong Lin
  • Svetlozar T. Rachev
Article

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.

Keywords

Option pricing Hedging Stochastic volatility Continuous Markov chain Regime-switching model Lévy process Esscher transform 

JEL Classification

C6 G11 G12 G13 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Young Shin Kim
    • 1
  • Frank J. Fabozzi
    • 2
  • Zuodong Lin
    • 3
  • Svetlozar T. Rachev
    • 1
    • 4
    • 5
  1. 1.Department of Statistics, Econometrics and Mathematical Finance, School of Economics and Business EngineeringKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.EDHEC Business SchoolNew YorkUSA
  3. 3.HECTOR School of Engineering and Management, International DepartmentKarlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Department of Applied Mathematics and StatisticsStony Brook UniversityStony BrookUSA
  5. 5.FinAnalyticaSeattleGermany

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