Estimation of partial differential equations with applications in finance

Kristensen, Dennis (2004) Estimation of partial differential equations with applications in finance. Financial Markets Group Discussion Papers (499). Financial Markets Group, The London School of Economics and Political Science, London, UK.

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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.

Item Type:	Monograph (Discussion Paper)
Official URL:	https://www.fmg.ac.uk/
Additional Information:	© 2004 The Author
Divisions:	Financial Markets Group
Subjects:	H Social Sciences > HG Finance H Social Sciences > HB Economic Theory
JEL classification:	C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C22 - Time-Series Models C - Mathematical and Quantitative Methods > C3 - Econometric Methods: Multiple; Simultaneous Equation Models; Multiple Variables; Endogenous Regressors > C32 - Time-Series Models
Date Deposited:	06 Aug 2009 08:42
Last Modified:	11 Dec 2024 18:38
URI:	http://eprints.lse.ac.uk/id/eprint/24738

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