Volatility and GMM: Monte Carlo studies and empirical estimations

In this paper we examine small sample properties of a generalized method of moments (GMM) estimation using Monte Carlo simulations. We assume that the generated time series describe the stochastic variance rate of a stock index. We use a mean reverting square-root prooess to simulate the dynamics of this instantaneous variance rate. The generated time series consist of 63, 250, and 1000 data points, respectively. They are used to estimate the Parameters of the assumed variance rate process by applying GMM. The results obtained are described and compared to our estimates from empirical volatility data. We use the German volatility index VDAX, historical volatilities of the German stock index DAX over 10, 22 and 33 trading days as well as daily volume data of the German stock market.