Estimating the Wishart Affine Stochastic Correlation Model Using the Empirical Characteristic Function

Abstract

In this paper, we present and discuss the estimation of the Wishart Affine Stochastic Correlation (WASC) model introduced in Da Fonseca et al. (2006) under the historical measure. We review the main estimation possibilities for this continuous time process and provide elements to show that the utilization of empirical characteristic function-based estimates is advisable as this function is exponential affine in the WASC case. We thus propose to use the estimation strategy presented in Carrasco et al. (2003), using a continuum of moment conditions based on the characteristic function. We investigate the behavior of the estimates through Monte Carlo simulations. Then, we present the estimation results obtained using a dataset of equity indexes: SP500, FTSE, DAX and CAC. On the basis of these results, we show that the WASC captures many of the known stylized facts associated with financial markets, including the negative correlation between stock returns and volatility. It also helps reveal interesting patterns in the studied indexes'covariances and their correlation dynamics.

Keywords: Wishart Process, Empirical Characteristic Function, Stochastic Correlation

JEL Classification: C32, C51, G12, G15