Abstract
Abstract Parametric mortality models permit detailed analysis of risk factors for actuarial work. However, finite data volumes lead to uncertainty over parameter estimates, which in turn gives rise to mis-estimation risk of financial liabilities. Mis-estimation risk can be assessed on a run-off basis by valuing the liabilities with alternative parameter vectors consistent with the covariance matrix. This run-off approach is especially suitable for tasks like pricing portfolio transactions, such as bulk annuities, longevity swaps or reinsurance treaties. However, a run-off approach does not fully meet the requirements of regulatory regimes that view capital requirements through the prism of a finite horizon, such as Solvency II’s one-year approach. This paper presents a methodology for viewing mis-estimation risk over a fixed time frame, and results are given for a specimen portfolio. As expected, we find that time-limited mis-estimation capital requirements increase as the horizon is lengthened or the discount rate is reduced. However, we find that much of the so-called mis-estimation risk in a one-year value-at-risk assessment can actually be driven by idiosyncratic variation, rather than parameter uncertainty. This counter-intuitive result stems from trying to view a long-term risk through a short-term window. As a result, value-at-risk mis-estimation reserves are strongly correlated with idiosyncratic risk. We also find that parsimonious models tend to produce lower mis-estimation risk than less-parsimonious ones.
Highlights
Introduction and MotivationWhen pricing or reserving for a block of insurance contracts, mortality assumptions are commonly divided into a minimum of two separate components: (i) the current level of mortality rates and (ii) projection of future trends
5 outlines how multi-factor mortality models are structured, while section 6 looks at specimen results over various horizons; section 7 considers what could be used as the best-estimate liability; section 8 considers the impact of liability concentration in a small proportion of lives, while section 9 examines the role played by portfolio size; section considers the sensitivity to discount rate, while section looks at variation by mortality law; section considers the correlation between adverse idiosyncratic risk and mis-estimation risk over the same horizon, while section concludes
We find that the resulting capital requirements for short time horizons are very different from a run-off approach that might be used for pricing
Summary
When pricing or reserving for a block of insurance contracts, mortality assumptions are commonly divided into a minimum of two separate components: (i) the current level of mortality rates and (ii) projection of future trends. This paper is concerned with the first basis element, i.e. the current level of mortality rates in a portfolio and the estimation risk thereof. These risks – sampling error and concentration of liabilities – combine to produce uncertainty over the current mortality rates and a magnified impact on the value of the liabilities. This uncertainty is variously labelled mis-estimation risk or level risk. This paper adapts the pricing mis-estimation methodology of Richards (2016) to frame mis-estimation risk over a short time horizon like 1–5 years. 5 outlines how multi-factor mortality models are structured, while section 6 looks at specimen results over various horizons; section 7 considers what could be used as the best-estimate liability; section 8 considers the impact of liability concentration in a small proportion of lives, while section 9 examines the role played by portfolio size; section considers the sensitivity to discount rate, while section looks at variation by mortality law; section considers the correlation between adverse idiosyncratic risk and mis-estimation risk over the same horizon, while section concludes
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