Likelihood-based inference for a class of multivariate diffusions with unobserved paths

Abstract

This document is the author's final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher's version if you wish to cite from it. Likelihood-based Inference for a Class of Multivariate Diffusions with Unobserved Paths Konstantinos Kalogeropoulos May 18, 2007Abstract This paper presents a Markov chain Monte Carlo algorithm for a class of multivariate diffusion models with unobserved paths. This class is of high practical interest as it includes most diffusion driven stochastic volatility models. The algorithm is based on a data augmentation scheme where the paths are treated as missing data. However, unless these paths are transformed so that the dominating measure is independent of any parameters, the algorithm becomes reducible. The methodology developed in Roberts and Stramer (2001 Biometrika 88(3):603-621) circumvents the problem for scalar diffusions. We extend this framework to the class of models of this paper by introducing an appropriate reparametrisation of the likelihood that can be used to construct an irreducible data augmentation scheme. Practical implementation issues are considered and the methodology is applied to simulated data from the Heston model.

Likelihood-based inference for correlated diffusions

“…Consequently, as shown in Kalogeropoulos (2007), it suffices to transform v t itself to unit volatility.…”

An MCMC Algorithm for Parameter Estimation in Signals with Hidden Intermittent Instability

“…Since the prior distribution for α mis (·) is an OU process, we experimented simulating OU paths with very limited success. It is well known that independent proposal distributions for Metropolis-Hastings algorithms are severely inefficient [25,34]. Our best implementation resulted in acceptance rates below 0.1%, indicating that the sampler fails to explore the posterior distribution properly.…”

“…Other related work and improved algorithms for diffusion models are found in [1,8,9,11,13,25,32,35,36,37]. However, extra effort is required to handle intermittency and unresolved processes.…”

Quasi-maximum likelihood estimation of multivariate diffusions

“…Recent developments include nonparametric method in Bianchi (2007), Markov chain Monte Carlo method in Kalogeropoulos (2007) and Golightly and Wilkinson (2008), and Hermite polynomials approximation in Aït-Sahalia (2008). The method in Aït-Sahalia (2008) offers a closed-form expansion for the transition density and yields high numerical precision for a large class of SDEs.…”