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

101 Pages Posted: 27 Nov 2019

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

Queen's University Belfast; Queen's University Belfast - Queen's Management School

Date Written: November 15, 2019

Abstract

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.

Keywords: Bayesian decision theory; Value-at-Risk; Backtesting; Annuity pricing; 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 (November 15, 2019). 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

Queen's University Belfast ( email )

25 University Square
Belfast, BT7 1NN
Ireland

Queen's University Belfast - Queen's Management School ( email )

Riddel Hall
185 Stranmillis Road
Belfast, BT9 5EE
United Kingdom

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