Maximum likelihood estimation of mean reverting …

Maximumlikelihood estimationofmeanrevertingprocessesJos e CarlosGarc a frequently usedmodelsin instance,somecommodity prices(or theirlogarithms)are frequently believed to revert to somelevel parameterknowledge,basedon economicanalysisof the forcesat play, is perhapsthe mostmeaningfulchannelfor model ,databasedmethods are oftenneededto complement andvalidatea meanreverting(OUMR)model is a Gaussianmodel well suitedfor maximumlikelihood (ML)methods. Alternative methods includeleastsquares(LS)regressionof discreteautoregressive versionsof the OUMR model andmethods of moments (MM).Each methodhas advantagesand instance,LS methods may not always yielda reasonableparameterset (see Chapter3 of Dixitand Pindyck[2]) and methods of moments lack the desirableoptimality propertiesof ML or LS Maximum - likelihood (ML)methodologyfor parameterestimationof1-dimensionalOrnste in-Uhlenbeck (OR) ,our methodol-ogy ultimatelyrelieson a one-dimensionalsearch which greatlyfacilitatesestimationand easilyaccommodtesmissingor unevenlyspaced(time-wise) meanreverting(OUMR)processgiven by thestochasticdifferentialequation(SDE)d x(t) = ( x x(t))dt+ dB(t);x(0)=x0(1)forconstants x, andx0andwhereB(t) is thismodeltheprocessx(t) fluctuatesrandomly, buttendsto revertto somefundamentallevel x.

Maximum likelihood estimation of mean reverting processes Jos e Carlos Garc a Franco Onward, Inc. jcpollo@onwardinc.com Abstract Mean reverting processes are frequently used models in real options.

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  Name, Processes, Estimation, Likelihood estimation of mean reverting, Likelihood, Reverting, Likelihood estimation of mean reverting processes

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