Perturbed Brownian motion and its application to Parisian option pricing
Dassios, A.
& Wu, S.
(2010).
Perturbed Brownian motion and its application to Parisian option pricing.
Finance and Stochastics,
14(3), 473-494.
https://doi.org/10.1007/s00780-009-0113-0
& Wu, S.
(2010).
Perturbed Brownian motion and its application to Parisian option pricing.
Finance and Stochastics,
14(3), 473-494.
https://doi.org/10.1007/s00780-009-0113-0
In this paper, 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.