Simulation of jump diffusions and the pricing of options

DiCesare, Joe; McLeish, D. L.

doi:10.1016/j.insmatheco.2008.06.001

Cited by 5 publications

(1 citation statement)

References 31 publications

(43 reference statements)

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“…There are ways to further accelerate this algorithm: First, a parallelization of Monte-Carlo simulations can very easily be implemented. Secondly, there are many variance reduction techniques to further (significantly) accelerate the algorithm (see, e.g., [10,31,42] on the single barrier algorithm). Figure 2 further examines the discretization bias of the two algorithms.…”

Section: Digital First-touch Optionsmentioning

confidence: 99%

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

Fernández

Hieber

Scherer

2013

Monte Carlo Methods and Applications

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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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Section: Digital First-touch Optionsmentioning

confidence: 99%