Filtering and Likelihood Estimation of Latent Factor Jump-Diffusions with an Application to Stochastic Volatility Models

28 Pages Posted: 11 Jun 2015

See all articles by Francesco Esposito

Francesco Esposito

Dublin City University Business School

Mark Cummins

Dublin City University Business School

Date Written: June 11, 2015

Abstract

In this article we use a partial integral-differential approach to construct and extend a non-linear filter to include jump components in the system state. We employ the enhanced filter to estimate the latent state of multivariate parametric jump-diffusions. The devised procedure is flexible and can be applied to non-affine diffusions as well as to state dependent jump intensities and jump size distributions. The particular design of the system state can also provide an estimate of the jump times and sizes. With the same approch by which the filter has been devised, we implement an approximate likelihood for the parameter estimation of models of the jump-diffusion class. In the development of the estimation function, we take particular care in designing a simplified algorithm for computing. The likelihood function is then characterised in the application to stochastic volatility models with jumps. In the empirical section we validate the proposed approach via Monte Carlo experiments. We deal with the volatility as an intrinsic latent factor, which is partially observable through the integrated variance, a new system state component that is introduced to increase the filtered information content, allowing a closer tracking of the latent volatility factor. Further, we analyse the structure of the measurement error, particularly in relation to the presence of jumps in the system. In connection to this, we detect and address an issue arising in the update equation, improving the system state estimate.

Keywords: latent state-variables, non-linear filtering, finite difference method, multi-variate jump-diffusions, likelihood estimation

JEL Classification: c13

Suggested Citation

Esposito, Francesco and Cummins, Mark, Filtering and Likelihood Estimation of Latent Factor Jump-Diffusions with an Application to Stochastic Volatility Models (June 11, 2015). Available at SSRN: https://ssrn.com/abstract=2617144 or http://dx.doi.org/10.2139/ssrn.2617144

Francesco Esposito (Contact Author)

Dublin City University Business School ( email )

Dublin 9
Ireland

Mark Cummins

Dublin City University Business School ( email )

Dublin 9
Ireland

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