Bayesian Value-at-Risk Backtesting: The Case of Annuity Pricing

We propose a new Unconditional Coverage backtest for VaR-forecasts under a Bayesian framework that significantly minimise the direct and indirect effects of p-hacking or other biased outcomes in decision-making, in general. Especially, after the global financial crisis of 2007-09, regulatory demands from Basel III and Solvency II have required a more strict assessment setting for the internal financial risk models. Here, we employ linear and nonlinear Bayesianised variants of two renowned mortality models to put the proposed backtesting technique into the context of annuity pricing. In this regard, we explore whether the stressed longevity scenarios are enough to capture the experienced liability over the foretasted time horizon. Most importantly, we conclude that our Bayesian decision theoretic framework quantitatively produce a strength of evidence favouring one decision over the other.