| Time-varying volatility plays an important role in modern financial markets. The stochastic volatility models are appealing in intuitive and practical usage as an alternative to ARCH/GARCH type models which deal with only a deterministic volatility factor. Frequentist methods have been mainly used for model fitting of the stochastic volatility models. Markov Chain Monte Carlo methods, however, provide more flexible ways in estimating the underlying volatilities as well as model parameters. In MCMC procedures, we utilize the sequential importance sampling method, which is a powerful and convenient tool to tackle the high-dimensional problems like stochastic volatility. Our methods are applied to different forms of financial models such as stochastic volatility models for stock price processes and interest rate term structure models. We also deal with the option pricing formula with stochastic volatility using the sequential importance sampling based MCMC method. In particular, certain Gaussian approximations are embedded into each iteration of MCMC, which significantly reduce the computational intensity. The detailed computational algorithms and results are provided. |
