Stochastic volatility in asset prices estimation with simulated maximum likelihood

Abstract

The stochastic volatility model is used to estimate daily asset price dynamics. The model is estimated by integrating latent volatility out of the joint density of prices and volatility to obtain the marginal density of prices. Due to high number of dimensions of the integral, no conventional integration technique is applicable. A Monte Carlo method, called simulated maximum likelihood, is used to obtain the marginal density, where the latent variable is simulated conditional on available information. The model is estimated by 2022 observations from the S & P 500 index. For comparison ARCH type models are estimated with the same data.