Simulation Monte Carlo methods in extended stochastic volatility models

Abstract

A new technique for nonlinear state and parameter estimation of discrete time stochastic volatility models is developed. Algorithms of Gibbs sampler and simulation filters are used to construct a simulation tool that reflects both inherent model variability and parameter uncertainty. The proposed chain converges to equilibrium enabling the estimation of unobserved volatilities and unknown model parameter distributions. The estimation algorithm is illustrated using numerical examples.

Pension Fund Model Design and State Estimation

“…There are three main approaches to design the global analytical filters for non-linear stochastic systems. The analytical approach based on the model linearization and Gaussian sum approximation of probability density function Sorenson andAlspach (1971) andŠimandl andKrálovec (2000), the numerical approach to solution of the Bayesian recursive relations leading to the grid base filters Bucy andSenne (1971) andŠimandl et al (2002) and the simulation approach using the Monte Carlo approximation Liu andChen (1998) andŠimandl andSoukup (2002). These approaches generate probability density function as a result of the estimation.…”