Abstracts

Value-at-Risk (VaR) models are an essential tool for risk management in the banking industry. We use Bayesian statistics methods to evaluate the performance of VaR models. We compare the results produced by Bayesian methods with the results given by classical methods. We find that the posterior probability density function for the probability of exceeding VaR is skewed to the right. The probability of observing a loss larger than VaR is larger than 50\%. Regulators advocate conservatism in estimating VaR but VaR models are producing VaR estimates which are biased towards optimism. Classical backtesting methods presently used don’t reveal this bias but Bayesian methods can do it.