Abstract
Continuous-time Markov processes are typically defined by stochastic differential equations, describing the evolution of one or more state variables. Maximum likelihood estimation of the model parameters to historical observations is only possible when at least one of the state variables is observable. In these cases, the form of the transition function corresponding to the stochastic differential equations must be known to assess the efficacy of fitting a continuous model to discrete samples. This paper makes two contributions: (i) we describe a new R package MLEMVD for calibrating general multi-variate diffusions models using maximum likelihood estimates; and (ii) we present an algorithm for calibrating the Heston model to option prices using maximum likelihood estimation and assess the robustness of the approach using Monte Carlo simulation.
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