Le vendredi 4 novembre 2011, 15:30, salle 1205 du Pavillon Burnside.

*A Bayesian method of parametric inference for diffusion processes*

Martin Lysy, Harvard University

Diffusion processes have been used to model a multitude of continuous-time phenomena in Engineering and the Natural Sciences, and as in this case, the volatility of financial assets. However, parametric inference has long been complicated by an intractable likelihood function. For many models the most effective solution involves a large amount of missing data for which the typical Gibbs sampler can be arbitrarily slow. On the other hand, joint parameter and missing data proposals can lead to a radical improvement, but their acceptance rate tends to scale exponentially with the number of observations.

We consider here a novel method of dividing the inference process into separate data batches, each small enough to benefit from joint proposals, to be processed consecutively. A filter combines batch contributions to produce likelihood inference based on the whole dataset. Although the result is not always unbiased, it has very low variability, often achieving considerable accuracy in a short amount of time. We present an example using Heston’s popular model for option pricing, but much of the methodology can be extended beyond diffusions to Hidden Markov and other State-Space models.