Estimation of Stochastic Covariance Models using a Continuum of Moment Conditions

We describe the implementation of a parameter estimation method suitable for models commonly used in quantitative finance. The Continuum - Generalized Method of Moments (CGMM) is a Generalized Method of Moments (GMM) type of methodology that applies a continuum of moment conditions to achieve efficiency. Instead of the transition density, the more commonly available conditional characteristic function is used for estimation. We apply CGMM to two stochastic covariance models, the Wishart Affine Stochastic Correlation (WASC) model and the Principal Components Stochastic Volatility (PCSV) model. This illustrates the power of CGMM as stochastic covariance models are generally hard to estimate. The estimation method is implemented in Matlab.