Exploring the Dependence between Mortality and Market Risks

In this paper, we develop a statistical approach to explore empirically the dependence between risks in the extremes. We apply it to study the dependence between mortality and market risks. With data for 6 developed countries, extending over 80 years, we pick the worst 10 years of mortality and compare their averages to the whole sample averages. We observe a reduction of the performance of some financial variables and an increase in correlation, but the effect remains weak and difficult to assess statistically. Moreover, our samples do not contain any significant pandemic outbreak, which limits our ability to explore very extreme events. To complement this study, we put in the appendix an econometric study by Philippe Trainar who examines the dynamic consequences of the Spanish Flu on the US market. He concludes that on a one year time horizon, he cannot detect a signi-ficant effect. This study shows how we could conduct a wider analysis if we had more data with higher frequency like monthly data. Exploring the Dependence between Mortality and Market Risks By Michel Dacorogna* and Meitner Cadena** April 2015 N°33 Texts appearing in SCOR Papers are the responsibility of their authors alone. In publishing such articles, SCOR takes no position on the opinions expressed by the authors in their texts and disclaims all responsibility for any opinions, incorrect information or legal errors found therein. * SCOR SE ** UPMC & CREAR-ESSEC Paris Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background