An ABC approach for CAViaR models with asymmetric kernels

Abstract

ABSTRACTThe Value at Risk (VaR) is a risk measure that is widely used by financial institutions to allocate risk. Optimal conditional VaR estimates are typically generated using a likelihood function based on the check-loss function. However, issues such as VaR's bias estimation and asymmetric financial decision-making, based on the sign of the forecast error, can result in the use of combined losses or of intractable likelihood functions. In such cases, likelihood function intractability gives ground for Bayesian inference using likelihood-free methods such as the Approximate Bayesian Computation (ABC) one. This method generates posterior estimates when the likelihood function is analytically unavailable. Here, we introduce a novel ABC-MCMC algorithm based on asymmetric kernel density functions that allows for the asymmetric decision-making rule used in VaR estimation. We illustrate this method in CAViaR models where VaR is forecast using simulated and real financial data series.