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

European Journal of Operational Research, Volume 293, Issue 2, pp. 786-801, 1 September 2021, DOI 10.1016/j.ejor.2020.12.051

111 Pages Posted: 27 Nov 2019 Last revised: 18 Apr 2021

See all articles by Melvern Leung

Melvern Leung

Monash University - Department of Econometrics & Business Statistics

Youwei Li

Hull University Business School

Athanasios A. Pantelous

Monash University - Department of Econometrics & Business Statistics

Samuel Vigne

Trinity College (Dublin) - Trinity Business School

Date Written: December 14, 2020

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

Suggested Citation

Leung, Melvern and Li, Youwei and Pantelous, Athanasios A. and Vigne, Samuel, Bayesian Value-at-Risk Backtesting: The Case of Annuity Pricing (December 14, 2020). European Journal of Operational Research, Volume 293, Issue 2, pp. 786-801, 1 September 2021, DOI 10.1016/j.ejor.2020.12.051, Available at SSRN: https://ssrn.com/abstract=3487386 or http://dx.doi.org/10.2139/ssrn.3487386

Melvern Leung

Monash University - Department of Econometrics & Business Statistics ( email )

900 Dandenong Road
Caulfield East, 3145
Australia

Youwei Li

Hull University Business School ( email )

University of Hull
Hull, HU6 7RX
United Kingdom

Athanasios A. Pantelous (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

Wellington Road
Clayton, Victoria 3168
Australia

Samuel Vigne

Trinity College (Dublin) - Trinity Business School ( email )

Aras an Phiarsaigh
College Green
Dublin, Leinster D2
Ireland

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