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

Konstantinos Dareiotis; Erik Ekström

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arXiv · 1706.06000

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

Konstantinos Dareiotis·Erik Ekström

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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 important applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models.

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Konstantinos Dareiotis, Erik Ekström. 2017-06-19. Density symmetries for a class of 2-D diffusions with applications to finance. https://arxiv.org/abs/1706.06000

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