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 languageEnglish
Pages (from-to)1069-1088
Number of pages20
JournalMathematical Finance
Volume27
Issue number4
Early online date19 May 2016
DOIs
Publication statusPublished - Oct 2017

Keywords

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

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