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

Abstract

We propose new Unconditional, Independence and Conditional Coverage VaR-forecast backtests for the case of annuity pricing under a Bayesian framework that significantly minimise the direct and indirect effects of $p$-hacking or other biased outcomes in decision-making, in general. As a consequence of the global financial crisis during 2007--09, regulatory demands arising from Solvency II has required a stricter assessment setting for the internal financial risk models of insurance companies. To put our newly proposed backtesting technique into practice we employ linear and nonlinear Bayesianised variants of two typically used mortality models in the context of annuity pricing. In this regard, we explore whether the stressed longevity scenarios are enough to capture the experienced liability over the forecasted time horizon. Most importantly, we conclude that our Bayesian decision theoretic framework quantitatively produce a strength of evidence favouring one decision over the other.

Keywords: Decision analysis; Value-at-Risk; Backtesting; Bayesian framework; Longevity risk

JEL Classification: C11, C12, C44, G13, G22, G23, G17