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Geometric step options and Lévy models: Duality, PIDEs, and semi-analytical pricing

Farkas, Walter; Mathys, Ludovic (2022). Geometric step options and Lévy models: Duality, PIDEs, and semi-analytical pricing. Frontiers of Mathematical Finance, 1(1):1-51.

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 duality 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.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Finance
Dewey Decimal Classification:330 Economics
Scope:Discipline-based scholarship (basic research)
Language:English
Date:March 2022
Deposited On:28 Jun 2022 07:01
Last Modified:19 Sep 2024 03:37
Publisher:AIMS Press
ISSN:2769-6715
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.3934/fmf.2021001
Official URL:https://doi.org/10.3934/fmf.2021001
Other Identification Number:merlin-id:21827
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