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Perturbed Brownian motion and its application to Parisian option pricing

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Abstract

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.

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Authors and Affiliations

  1. Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    Angelos Dassios & Shanle Wu

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  1. Angelos Dassios
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  2. Shanle Wu
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Correspondence to Angelos Dassios.

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

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  • DOI: https://doi.org/10.1007/s00780-009-0113-0

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