Book Description

Stochastic Volatility (SV) models play an integral role in modeling time varying volatility, with widespread application in finance. Due to the absence of a closed form likelihood function, estimation is a challenging problem. In the presence of outliers, and the high kurtosis prevalent in financial data, robust estimation techniques are desirable. Also, in the context of risk assessment when the underlying model is SV, computing the one step ahead predictive return densities for Value at Risk (VaR) calculation entails a numerically indirect procedure. The Quantile Regression (QR) estimation is an increasingly important tool for analysis, which helps in fitting parsimonious models in lieu of full conditional distributions. We propose two methods (i) Regression Quantile Method of Moments (RQMM) and (ii) Regression Quantile - Kalman Filtering method (RQ-KF) based on the QR approach that can be used to obtain robust SV model parameter estimates as well as VaR estimates. The RQMM is a simulation based indirect inference procedure where auxiliary recursive quantile models are used, with gradients of the RQ objective function providing the moment conditions. This was motivated by the Efficient Method of Moments (EMM) approach used in SV model estimation and the Conditional Autoregressive Value at Risk (CAViaR) method. An optimal linear quantile model based on the underlying SV assumption is derived. This is used along with other CAViaR specifications for the auxiliary models. The RQ-KF is a computationally simplified procedure combining the QML and QR methodologies. Based on a recursive model under the SV framework, quantile estimates are produced by the Kalman filtering scheme and are further refined using the RQ objective function, yielding robust estimates. For illustration purposes, comparison of the RQMM method with EMM under different data scenarios show that RQMM is stable under model misspecification, presence of outliers and heavy-tailedness. Comparison of the RQ.