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DENSITY OF SKEW BROWNIAN MOTION AND ITS FUNCTIONALS WITH APPLICATION IN FINANCE |
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| Authors: | Alexander Gairat Vadim Shcherbakov |
| Affiliation: | 1. Numerix, Moscow;2. Royal HollowayUniversity of London |
| 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. |
| Keywords: | Skew Brownian motion local volatility model displaced diffusion local time occupation time simple random walk option pricing |
