Estimating parameters in diffusion processes using an approximate maximum likelihood approach
(2007) In Annals of Operations Research 151(1). p.269288 Abstract
 We present an approximate Maximum Likelihood estimator for univariate Ito 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 FokkerPlanck 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... (More)
 We present an approximate Maximum Likelihood estimator for univariate Ito 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 FokkerPlanck 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 CoxIngersollRoss model and a nonlinear extension of the ChanKarolyiLongstaffSanders 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 simulationbased estimator and a CrankNicholson scheme applied to the FokkerPlanck equation, and the proposed estimator is still competitive. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/674359
 author
 Lindström, Erik ^{LU}
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 CoxIngersollRoss model, nonlinear CKLS model, CrankNicholson scheme, approximate likelihood function, DurhamGallant estimator
 in
 Annals of Operations Research
 volume
 151
 issue
 1
 pages
 269  288
 publisher
 Kluwer
 external identifiers

 wos:000244450800013
 scopus:33847265348
 ISSN
 15729338
 DOI
 10.1007/s1047900601264
 language
 English
 LU publication?
 yes
 id
 25da36e070dc4c7f9fb88b182a2fd566 (old id 674359)
 date added to LUP
 20071213 12:54:52
 date last changed
 20180107 09:08:08
@article{25da36e070dc4c7f9fb88b182a2fd566, abstract = {We present an approximate Maximum Likelihood estimator for univariate Ito 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 FokkerPlanck 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 CoxIngersollRoss model and a nonlinear extension of the ChanKarolyiLongstaffSanders 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 simulationbased estimator and a CrankNicholson scheme applied to the FokkerPlanck equation, and the proposed estimator is still competitive.}, author = {Lindström, Erik}, issn = {15729338}, keyword = {CoxIngersollRoss model,nonlinear CKLS model,CrankNicholson scheme,approximate likelihood function,DurhamGallant estimator}, language = {eng}, number = {1}, pages = {269288}, publisher = {Kluwer}, series = {Annals of Operations Research}, title = {Estimating parameters in diffusion processes using an approximate maximum likelihood approach}, url = {http://dx.doi.org/10.1007/s1047900601264}, volume = {151}, year = {2007}, }