Petros Dellaportas (University College London)

High dimensional jump processes with stochastic volatility

We deal with the problem of identifying jumps in multiple financial time series using the stochastic volatility model combined with a jump process. We develop efficient MCMC algorithms to perform Bayesian inference for the parameters and the latent states of the proposed models. In the univariate case we use an homogeneous compound Poisson process for the modelling of the jump component. In the multivariate case  we adopt an inhomogeneous Poisson process, with intensity which is also a stochastic process varying across time and economic sectors and markets. A Gaussian process is used as prior distribution for the intensity of the Poisson process. This model is known as doubly stochastic Poisson process or Gaussian Cox process. The efficiency of the proposed algorithms is compared with existing MCMC algorithms. Our methodology is tested through simulation based experiments and applied on 600 stock daily returns of Euro STOXX index over a period of 10 years.