WIAS Preprint No. 2191, (2015)

Option pricing in affine generalized Merton models



Authors

  • Bayer, Christian
  • Schoenmakers, John G. M.

2010 Mathematics Subject Classification

  • 91G60 65C30

Keywords

  • Affine processes, Merton jump-model, approximate affine characteristic function

Abstract

In this article we consider affine generalizations of the Merton jump diffusion model Merton (1976) and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in Belomestny, Kampen, Schoenmakers (2009). We conclude with some numerical examples.

Appeared in

  • J.G.M. Schoenmakers, Ch. Bayer, Option pricing in affine generalized Merton models, J. Kallsen, A. Papapantoleon , eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing , Switzerland, 2016, pp. 219--239

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