GLOBALLY OPTIMAL PARAMETER ESTIMATES FOR NONLINEAR DIFFUSIONS

Abstract. This paper introduces a novel expected maximum likelihood (EML) algorithm
for inferring the parameters of discretely observed diffusion processes. The approach
is applicable to models specified by non-linear stochastic differential equations with
constant volatility that are linear in the model parameters. In this setting the globally
optimal parameters are obtained in a single step by solving a linear system. The EML
algorithm is simple and fast in execution and can therefore be applied to models with
state-dependent volatility to reduce the dimensionality of the parameter space and to
explore the likelihood function of the model. Simulation studies to test the EML
algorithm show that it performs well when compared with exact maximum likelihood
estimation algorithms as well as closed-form likelihood expansions.

C++ code that implements the EML algorithm for the square-root process, together with
the implied volatility (VXO) data used in the paper, is available here.

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