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

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  • Leung, Melvern
  • Li, Youwei
  • Pantelous, Athanasios
  • Vigne, Samuel

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.

Suggested Citation

  • Leung, Melvern & Li, Youwei & Pantelous, Athanasios & Vigne, Samuel, 2019. "Bayesian Value-at-Risk Backtesting: The Case of Annuity Pricing," MPRA Paper 101698, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:101698
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    References listed on IDEAS

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    Cited by:

    1. Portugal, Luís & Pantelous, Athanasios A. & Verrall, Richard, 2021. "Univariate and multivariate claims reserving with Generalized Link Ratios," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 57-67.

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    More about this item

    Keywords

    Bayesian decision theory; Value-at-Risk; Backtesting; Annuity pricing; Longevity risk;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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