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Estimation of partial differential equations with applications in finance

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  • Kristensen, Dennis

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.

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  • Kristensen, Dennis, 2004. "Estimation of partial differential equations with applications in finance," LSE Research Online Documents on Economics 24738, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:24738
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    Cited by:

    1. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
    2. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    3. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    4. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    5. Gospodinov, Nikolay & Hirukawa, Masayuki, 2012. "Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 595-609.
    6. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.

    More about this item

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance
    • J1 - Labor and Demographic Economics - - Demographic Economics

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