Asset pricing and volatility modeling take a center stage in financial econometrics. This talk concerns calibration of stochastic volatility models via Markov chain Monte Carlo (MCMC) methods based on returns and option data. With the presence of high-dimensional latent volatility processes, numerical integration for computing option prices is required at every time point and every iteration of MCMC. There is an urgent need for developing approximation schemes that reduce numerical integration from a high-dimensional space (of diffusion sample paths) to a low-dimensional space (of 2D or 3D random vectors). We propose using bivariate Gaussian or gamma mixtures of Gaussian to approximate joint distributions of certain integrated volatilities and additive functionals in the lifetime of relevant options or other derivatives. When implementing those schemes to computation of various derivatives prices represented by generalized Black-Scholes formulas, they significantly improve the efficiency (speed/accuracy) of related MCMC algorithms. This will have an impact on a wide range of problems in financial econometrics.
Mon., November 12, 2007