Probabilistic Forecasts of Volatility and Its Risk Premia

• Activity Number: 653
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Worapree Maneesoonthorn*+
• Companies: Monash University
• Keywords: Stochastic Volatility ; Non-linear State Space Model ; Bayesian ; Variance Risk Premia ; Probabilistic Forecasts

Abstract

The object of this paper is to produce distributional forecasts of physical volatility and its associated risk premia using a non-Gaussian, non-linear state space approach. Option and spot market information on the unobserved variance process is captured by using dual `model-free' variance measures to define a bivariate observation equation in the state space model. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo algorithm that caters for the multiple sources of non-linearity in the model and the bivariate measure. The method is applied to empirical spot and option price data for the S&P500 index over the 1999 to 2008 period, with conclusions drawn about investors' required compensation for variance risk during the recent financial turmoil. The accuracy of the probabilistic forecasts of the observable variance measures is demonstrated, and compared with that of forecasts yielded by more standard time series models. To illustrate the benefits of the approach, the posterior distribution is augmented by information on returns to produce Value at Risk predictions, as well as being used to yield forecasts of prices of derivatives on volatility.