Density of Skew Brownian motion and its functionals with application in finance

Alexander Gairat; Vadim Shcherbakov

doi:10.1111/mafi.12120

Density of Skew Brownian motion and its functionals with application in finance

Alexander Gairat, Vadim Shcherbakov

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Abstract

We derive the joint density of a Skew Brownian motion, its last visit to the origin, its local and occupation times. The result enables us to obtain explicit analytical formulas for pricing European options under both a two‐valued local volatility model and a displaced diffusion model with constrained volatility.

Original language	English
Pages (from-to)	1069-1088
Number of pages	20
Journal	Mathematical Finance
Volume	27
Issue number	4
Early online date	19 May 2016
DOIs	https://doi.org/10.1111/mafi.12120
Publication status	Published - Oct 2017

Keywords

Skew Brownian motion, local volatility model, displaced diffusion, local time, occupation time, simple random walk, option pricing

Access to Document

10.1111/mafi.12120

Accepted ManuscriptAccepted author manuscript, 161 KB

http://onlinelibrary.wiley.com/doi/10.1111/mafi.12120/abstract

Cite this

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abstract = "We derive the joint density of a Skew Brownian motion, its last visit to the origin, its local and occupation times. The result enables us to obtain explicit analytical formulas for pricing European options under both a two‐valued local volatility model and a displaced diffusion model with constrained volatility.",

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