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 |
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Pages (from-to) | 1069-1088 |
Number of pages | 20 |
Journal | Mathematical Finance |
Volume | 27 |
Issue number | 4 |
Early online date | 19 May 2016 |
DOIs | |
Publication status | Published - Oct 2017 |
Keywords
- Skew Brownian motion, local volatility model, displaced diffusion, local time, occupation time, simple random walk, option pricing