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

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  • Dareiotis, Konstantinos
  • Ekström, Erik

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.

Suggested Citation

  • Dareiotis, Konstantinos & Ekström, Erik, 2019. "Density symmetries for a class of 2-D diffusions with applications to finance," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 452-472.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:2:p:452-472
    DOI: 10.1016/j.spa.2018.03.007
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2010. "Valuation equations for stochastic volatility models," Papers 1004.3299, arXiv.org, revised Dec 2011.
    3. Erik Ekstrom & Per Lotstedt & Johan Tysk, 2009. "Boundary Values and Finite Difference Methods for the Single Factor Term Structure Equation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 253-259.
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