Partial Differential Equation Approach Under Geometric Jump-Diffusion Process

Carl Chiarella, Xuezhong (Tony) He () and Christina Sklibosios Nikitopoulos
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Christina Sklibosios Nikitopoulos: University of Technology Sydney

Chapter Chapter 14 in Derivative Security Pricing, 2015, pp 295-314 from Springer

Abstract: 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.

Keywords: Jump-diffusion Process; Partial Integro-differential Equation; Jump Size Distribution; Underlying Asset Price; Derivative Securities (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-662-45906-5_14

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DOI: 10.1007/978-3-662-45906-5_14

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