Geometric Step Options with Jumps: Parity Relations, PIDEs, and Semi-Analytical Pricing

Walter Farkas and Ludovic Mathys
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Walter Farkas: University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zürich
Ludovic Mathys: University of Zurich - Department of Banking and Finance

No 20-11, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and derive various characterizations for both European-type and American-type geometric double barrier step options. In particular, we are able to obtain a jump-diffusion disentanglement for the early exercise premium of American-type geometric double barrier step contracts and its maturity-randomized equivalent as well as to characterize the diffusion and jump contributions to these early exercise premiums separately by means of partial integro-differential equations and ordinary integro-differential equations. As an application of our characterizations, we derive semi-analytical pricing results for (regular) European-type and American-type geometric down-and-out step call options under hyper-exponential jump-diffusion models. Lastly, we use the latter results to discuss the early exercise structure of geometric step options once jumps are added and to subsequently provide an analysis of the impact of jumps on the price and hedging parameters of (European-type and American-type) geometric step contracts.

Keywords: Geometric Step Options; American-Type Options; Lévy Markets; Jump-Diffusion Disentanglement; Maturity-Randomization (search for similar items in EconPapers)
JEL-codes: C32 C61 C63 G13 (search for similar items in EconPapers)
Pages: 49 pages
Date: 2020-03
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2011

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