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Density symmetries for a class of 2-D diffusions with applications to finance
Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2019 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 129, no 2, p. 452-472Article in journal (Refereed) Published
Abstract [en]

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. (C) 2018 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2019. Vol. 129, no 2, p. 452-472
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Probability Theory and Statistics
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URN: urn:nbn:se:uu:diva-376812DOI: 10.1016/j.spa.2018.03.007ISI: 000456229200004OAI: oai:DiVA.org:uu-376812DiVA, id: diva2:1290405
Available from: 2019-02-20 Created: 2019-02-20 Last updated: 2019-02-20Bibliographically approved

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Ekström, Erik

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