Title: Forecasting value at risk and expected shortfall using a dynamic omega ratio
Authors: James Taylor - University of Oxford (United Kingdom) [presenting]
Abstract: Value at Risk (VaR) and expected shortfall (ES) have become the standard measures of market risk. The recent development of joint scoring functions for the two measures enables joint models to be estimated. Previous work has shown promising results when an autoregressive model is used for the VaR, and the ES is modelled as the product of the VaR and a constant factor. We propose a time-varying multiplicative factor. It has previously been shown that the ES can be expressed as the product of an expectile and a constant multiplicative factor, which is a function of the expectile level. We rewrite this as the product of a quantile and a multiplicative factor that is a function of a time-varying expectile level. The expectile level is itself a simple function of the omega ratio, which is the ratio of expected gains to expected losses. This leads us to propose a new joint model in which the ES is modelled as the product of the VaR and a factor that is a function of a time-varying omega ratio, which we model using autoregressive expressions for the expected gain and expected loss. We provide empirical illustration using stock index returns.