NDLI: Estimating parameters in diffusion processes using an approximate maximum likelihood approach

Content Provider	Springer Nature Link
Author	Lindström, Erik
Copyright Year	2006
Abstract	We present an approximate Maximum Likelihood estimator for univariate Itô stochastic differential equations driven by Brownian motion, based on numerical calculation of the likelihood function. The transition probability density of a stochastic differential equation is given by the Kolmogorov forward equation, known as the Fokker-Planck equation. This partial differential equation can only be solved analytically for a limited number of models, which is the reason for applying numerical methods based on higher order finite differences.The approximate likelihood converges to the true likelihood, both theoretically and in our simulations, implying that the estimator has many nice properties. The estimator is evaluated on simulated data from the Cox-Ingersoll-Ross model and a non-linear extension of the Chan-Karolyi-Longstaff-Sanders model. The estimates are similar to the Maximum Likelihood estimates when these can be calculated and converge to the true Maximum Likelihood estimates as the accuracy of the numerical scheme is increased. The estimator is also compared to two benchmarks; a simulation-based estimator and a Crank-Nicholson scheme applied to the Fokker-Planck equation, and the proposed estimator is still competitive.
Starting Page	269
Ending Page	288
Page Count	20
File Format	PDF
ISSN	02545330
Journal	Annals of Operations Research
Volume Number	151
Issue Number	1
e-ISSN	15729338
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2006-11-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Approximate likelihood function Durham-Gallant estimator Crank-Nicholson scheme Cox-Ingersoll-Ross model Non-linear CKLS model Theory of Computation Combinatorics Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research

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