Review of Derivatives Research

, Volume 9, Issue 1, pp 1–35

Calibration and hedging under jump diffusion

  • C. He
  • J. S. Kennedy
  • T. F. Coleman
  • P. A. Forsyth
  • Y. Li
  • K. R. Vetzal
Article

Abstract

A jump diffusion model coupled with a local volatility function has been suggested by Andersen and Andreasen (2000). By generating a set of option prices assuming a jump diffusion with known parameters, we investigate two crucial challenges intrinsic to this type of model: calibration of parameters and hedging of jump risk. Even though the estimation problem is ill-posed, our results suggest that the model can be calibrated with sufficient accuracy. Two different strategies are explored for hedging jump risk: a semi-static approach and a dynamic technique. Simulation experiments indicate that each of these methods can sharply reduce risk exposure.

Keywords

Jump diffusion Calibration Static hedging Dynamic hedging 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • C. He
    • 1
  • J. S. Kennedy
    • 2
  • T. F. Coleman
    • 3
  • P. A. Forsyth
    • 4
  • Y. Li
    • 4
  • K. R. Vetzal
    • 5
  1. 1.J.P. Morgan Securities Inc.New York10017-2070USA
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  3. 3.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  4. 4.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  5. 5.Centre for Advanced Studies in FinanceUniversity of WaterlooWaterlooCanada

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