Density symmetries for a class of 2-D diffusions with applications to finance

Konstantinos Dareiotis and Erik Ekström

Stochastic Processes and their Applications, 2019, vol. 129, issue 2, 452-472

Abstract: We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding forward Kolmogorov equation problematic. We overcome this by extending a classical symmetry result for densities of one-dimensional diffusions to our case, thereby reducing the study of forward equations with exploding boundary data to the study of a related backward equation with non-exploding boundary data. We also discuss applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models.

Date: 2019
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DOI: 10.1016/j.spa.2018.03.007

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