DENSITY OF SKEW BROWNIAN MOTION AND ITS FUNCTIONALS WITH APPLICATION IN FINANCE

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 constrain...

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Bibliographic Details
Published inMathematical finance Vol. 27; no. 4; pp. 1069 - 1088
Main Authors Gairat, Alexander, Shcherbakov, Vadim
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.10.2017
Subjects
Brownian motion
Density
displaced diffusion
Finance
Functionals
local time
local volatility model
occupation time
option pricing
simple random walk
Skew Brownian motion
Volatility
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Summary: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.
Bibliography:The authors would like to thank the referees and the editors for comments that greatly improved the manuscript.
ISSN:0960-1627
1467-9965
DOI:10.1111/mafi.12120