Estimation of partial differential equations with applications in finance

Dennis Kristensen

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Linear parabolic partial differential equations (PDE’s) and diffusion models are closely linked through the celebrated Feynman-Kac representation of solutions to PDE’s. In asset pricing theory, this leads to the representation of derivative prices as solutions to PDE’s. We give a number of examples of this, including the pricing of bonds and interest rate derivatives. Very often derivative prices are calculated given preliminary estimates of the diffusion model for the underlying variable. We demonstrate that the derivative prices are consistent and asymptotically normally distributed under general conditions. We apply this result to three leading cases of preliminary estimators: Nonparametric, semiparametric and fully parametric ones. In all three cases, the asymptotic distribution of the solution is derived. Our general results have other applications in asset pricing theory and in the estimation of diffusion models; these are also discussed.

JEL-codes: C14 C22 C32 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2004-06
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http://eprints.lse.ac.uk/24738/ Open access version. (application/pdf)

Related works:
Journal Article: Estimation of partial differential equations with applications in finance (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:24738

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