Density symmetries for a class of 2-D diffusions with applications to finance |
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Authors: | Konstantinos Dareiotis Erik Ekström |
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Institution: | 1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany;2. Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden |
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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 applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models. |
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Keywords: | Corresponding author |
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