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Parameter estimation for forward Kolmogorov equation with application to nonlinear exchange rate dynamics
Author(s) -
Jäger Simon,
Kostina Ekaterina
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510347
Subject(s) - nonlinear system , stochastic differential equation , mathematics , diffusion , volatility (finance) , mathematical finance , computer science , differential equation , mathematical optimization , econometrics , mathematical analysis , economics , physics , thermodynamics , quantum mechanics , financial economics
Diffusion processes are widely used for mathematical modeling in finance e.g. in modeling foreign exchange rates. Stochastic differential equations describing diffusion processes are linked directly to the forward Kolmogorov equations. In order to calibrate the models, efficient algorithms identifying the system parameters are in demand. Taking into account nonlinear effects in volatility and drift and dependence on observed economical data, which are not directly modeled, one obtains problems which cannot be treated by standard numerical methods. The coefficients are rapidly oscillatory and strong instabilities may arise. To handle these problem we develop special numerical methods, which are used to simulate the nonlinear dynamics of exchange rates depending on economic data. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)