Density of skew Brownian motion and its functionals with application in finance. (English) Zbl 1411.91555

Gairat, Alexander; Shcherbakov, Vadim

Math. Finance 27, No. 4, 1069-1088 (2017).

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.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60J65	Brownian motion

Keywords:

skew Brownian motion; local volatility model; displaced diffusion; local time; occupation time; simple random walk; option pricing