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Partial Differential Equation Approach Under Geometric Jump-Diffusion Process

In: Derivative Security Pricing

Author

Listed:
  • Carl Chiarella

    (University of Technology Sydney)

  • Xue-Zhong He

    (University of Technology Sydney)

  • Christina Sklibosios Nikitopoulos

    (University of Technology Sydney)

Abstract

In this chapter we consider the solution of the integro-partial differential equation that determines derivative security prices when the underlying asset price is driven by a jump-diffusion process. We take the analysis as far as we can for the case of a European option with a general pay-off and the jump-size distribution is left unspecified. We obtain specific results in the case of a European call option and when the jump size distribution is log-normal. We illustrate two approaches to the problem. The first is the Fourier transform technique that we have used in the case that the underlying asset follows a diffusion process. The second is the direct approach using the expectation operator expression that follows from the martingale representation. We also show how these two approaches are connected.

Suggested Citation

  • Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Partial Differential Equation Approach Under Geometric Jump-Diffusion Process," Dynamic Modeling and Econometrics in Economics and Finance, in: Derivative Security Pricing, edition 127, chapter 0, pages 295-314, Springer.
    • Handle: RePEc:spr:dymchp:978-3-662-45906-5_14
    DOI: 10.1007/978-3-662-45906-5_14
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