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Perturbed Brownian motion and its application to Parisian option pricing. (English) Zbl 1226.91073
Summary: We study the excursion times of a Brownian motion with drift below and above a given level by using a simple two-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of path-dependent options such as Parisian options. Based on our results, we introduce a new type of Parisian options, single-barrier two-sided Parisian options, and give an explicit expression for the Laplace transform of its price formula.

91G20 Derivative securities (option pricing, hedging, etc.)
60J65 Brownian motion
60K15 Markov renewal processes, semi-Markov processes
60J27 Continuous-time Markov processes on discrete state spaces
Full Text: DOI
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