Maximum Likelihood Estimation for Integrated Diffusion Processes

Fernando Baltazar-Larios () and Michael Sørensen ()
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Fernando Baltazar-Larios: Universidad Nacional Autónoma de México, Instituto de Investigación en Matemáticas Aplicadas y en Sistemas
Michael Sørensen: University of Copenhagen, Department of Mathematical Sciences

A chapter in Contemporary Quantitative Finance, 2010, pp 407-423 from Springer

Abstract: Abstract We propose a method for obtaining maximum likelihood estimates of parameters in diffusion models when the data is a discrete time sample of the integral of the process, while no direct observations of the process itself are available. The data are, moreover, assumed to be contaminated by measurement errors. Integrated volatility is an example of this type of observations. Another example is ice-core data on oxygen isotopes used to investigate paleo-temperatures. The data can be viewed as incomplete observations of a model with a tractable likelihood function. Therefore we propose a simulated EM-algorithm to obtain maximum likelihood estimates of the parameters in the diffusion model. As part of the algorithm, we use a recent simple method for approximate simulation of diffusion bridges. In simulation studies for the Ornstein-Uhlenbeck process and the CIR process the proposed method works well.

Keywords: Maximum Likelihood Estimation; Stochastic Differential Equation; Sample Path; Stochastic Volatility; Milstein Scheme (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-03479-4_20

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DOI: 10.1007/978-3-642-03479-4_20

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