Double-barrier first-passage times of jump-diffusion processes

Lexuri Fernández 1 , Peter Hieber 2 , and Matthias Scherer 3
  • 1 University of the Basque Country UPV/EHU, Ekonomia Analisiaren Oinarriak II Saila, Lehendakari Agirre Hiribidea, 83, 48015 Bilbao, Spain
  • 2 Lehrstuhl für Finanzmathematik (M13), Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
  • 3 Lehrstuhl für Finanzmathematik (M13), Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany

Abstract.

Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Monte-Carlo simulation to obtain double-barrier first-passage time probabilities of a jump-diffusion process with arbitrary jump size distribution; extending single-barrier results by [Journal of Derivatives 10 (2002), 43–54]. In mathematical finance, the double-barrier first-passage time is required to price exotic derivatives, for example corridor bonus certificates, (step) double barrier options, or digital first-touch options, that depend on whether or not the underlying asset price exceeds certain threshold levels. Furthermore, it is relevant in structural credit risk models if one considers two exit events, e.g., default and early repayment.

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