  Jump stochastic volatility models are central to financial econometrics for
volatility forecasting, portfolio risk management, and derivatives pricing.
Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for
the sequential learning of volatility state variables and parameters, whereby
the investor must update all posterior and predictive densities as new
information arrives. We develop a particle filtering and learning algorithm to
sample posterior distribution in Merton's jump stochastic volatility. This
allows to filter spot volatilities and jump times, together with sequentially
updating (learning) of jump and volatility parameters. We illustrate our
methodology on Google's stock return. We conclude with directions for future
research.
