Likelihood-based inference for correlated diffusions

Konstantinos Kalogeropoulos (), Petros Dellaportas and Gareth O. Roberts

MPRA Paper from University Library of Munich, Germany

Abstract: We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorisation on the diffusion matrix. To deal with the likelihood unavailability, we generalise the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities.

Keywords: Markov chain Monte Carlo; Multivariate stochastic volatility; Multivariate CIR model; Cholesky Factorisation (search for similar items in EconPapers)
JEL-codes: C11 C13 C15 G12 (search for similar items in EconPapers)
Date: 2007
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ict
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Citations: View citations in EconPapers (2)

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Working Paper: Likelihood-based inference for correlated diffusions (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:5696

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