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Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency

Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency Katja Hanewald a,b,c , Thomas Post a,b,c , and Helmut Gründl a,b,c a Humboldt-Universität zu Berlin b Collaborative Research Center 649: Economic Risk c CASE - Center for Applied Statistics and Economics. Motivation.

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Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency

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  1. Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency Katja Hanewalda,b,c, Thomas Posta,b,c, and Helmut Gründla,b,c a Humboldt-Universität zu Berlin b Collaborative Research Center 649: Economic Risk c CASE - Center for Applied Statistics and Economics

  2. Motivation • Systematic deviations of actual mortality rates from assumed ones: threat to the financial stability of life insurers • Recent demographic study (Hanewald, 2009): Lee-Carter mortality index is significantly correlated with macroeconomic changes • Idea: Assess the overall impact of macroeconomic fluctuations on the financial stability of a life insurance company

  3. Preview of Results • Insolvency probabilities are considerably higher when dependencies between the mortality index ktand economic variables are taken into account • This result is robust to variations in: • the age of the insureds • the insurance portfolio size • the amount of equity capital • the asset allocation

  4. Contents • Literature Review • The Simulation Framework • Simulation Results • Conclusion

  5. Literature Review • Stochastic mortality modeling • Status quo summarized in Cairns, Blake, and Dowd (2008) • Lee-Carter (1992) model: “The earliest model and still the most popular” • Stochastic mortality in life-insurance portfolios • Dowd, Cairns, and Blake (2006), Hári et al. (2008), and Bauer and Weber (2008): impact of stochastic mortality on an insurer’s risk exposure • Gründl, Post, and Schulze (2006), Cox and Lin (2007), and Wang et al. (2008): natural hedging opportunities

  6. Literature Review • The impact of macroeconomic changes on mortality • Ruhm (2000): mortality rates in the U.S. fluctuate procyclically over the period 1972–1991 • Similar patterns observed for: • U.S., Spain, and Japan (Tapia Granados, 2005a, 2005b, 2008) • Germany (Neumayer, 2004, and Hanewald, 2008) • Sweden (Tapia Granados and Ionides, 2008) • 23 OECD countries, 1960–1997 (Gerdtham and Ruhm, 2006) • Especially: cardiovascular fatalities, influenza/pneunomia deaths (Ruhm, 2004, Tapia Granados, 2008)

  7. Literature Review • Hanewald (2009): “Mortality modeling: Lee-Carter and the macroeconomy” • Relationship between the Lee-Carter mortality index kt and changes in real GDP or unemployment rates • Six OECD countries, 1950–2005 • Results • Dkt significantly correlated with macroeconomic changes in Australia, Canada, Japan, and the United States • Structural change in that relationship at the beginning of the 1990s

  8. The Simulation Framework • Correlations between Dkt andreal GDP growth, United States Early 1970s: Dramatic decline in CVD mortality 1990s: Reduced mortality from tobacco and alcohol consumption, motor vehicle crashes, influenza and pneumonia Note: * P < 0.05,+P < 0.1 Ongoing: Substantial increase in deaths attributable to poor diet and lack of physical activity

  9. Contents • Literature Review • The Simulation Framework • Simulation Results • Conclusion

  10. Model misspecification risk The Simulation Framework • Goal: Assess the overall impact of macroeconomic fluctuations on a life insurer’s solvency situation • Stochastic dynamic asset-liability model • Both sides of the balance sheet react to macroeconomic changes • Target variable: Multi-period insolvency probability • Compare two versions of the model • Reduced correlation structure • Full correlation structure

  11. The Simulation Framework • Newly founded life insurance company • Writes I0 term-life contracts in t = 0 • Annual premium P • Death benefit B • Contract duration T • All insureds are of age x • Fixed proportion g of first year’s premium income raised as equity capital E0

  12. The Simulation Framework • Two lognormally-distributed investment opportunities • Stocks and bonds • Annually rebalanced asset portfolio • a [0, 1] constant fraction of assets invested in stocks • Fixed dividend ratio d • Claims and reserves calculated based on the realized mortality index

  13. The Simulation Framework • Mortality rates • Lee and Carter (1992): mx, t = exp(ax + bx ∙ kt) • Stochastic drivers of the model • Real GDP Dln(real GDPt) = mGDP + sGDP ∙eGDP, t • Stock returns rs, t = ms + ss ∙es, t • Bond returns rb, t = mb + sb ∙eb, t • Mortality index Dkt=  + sk ∙ek, t • Account for correlation structure between eGDP, t, es, t, eb, t,and ek, t

  14. The Simulation Framework • Calibration to empirical data • United States • 1989-2005 (Hanewald, 2009) • Data sources • Real GDP:U.S. Bureau of Economic Analysis • Stock/bond returns: Morningstar (2008) • Mortality rates: Human Mortality Database

  15. The Simulation Framework • Estimated parameters of stochastic processes

  16. Contents • Literature Review • The Simulation Framework • Simulation Results • Conclusion

  17. Simulation Results • Base scenario: term-life insurance, T = 10 years, B = $100,000, I0 = 10,000, males, age = 40 in t = 0 Ignoring correlations between kt and economic variables  underestimation of insolvency probabilities

  18. Simulation Results Increase in insolvency probabilities from switching to the full correlation scenario depends on bx • Vary initial age x

  19. = + 0.015 = + 10.5% = + 0.016 = + 53.1% Simulation Results • Vary size I0 of the insurance portfolio Underestimation risk more severe for larger portfolios

  20. Simulation Results The relative increase in risk is larger for higher initial amounts of equity capital. • Vary initial amount of equity E0

  21. Simulation Results Larger fraction of stocks induces higher exposure to unfavorable dependency between assets and liabilities • Vary stock proportion a

  22. Contents • Literature Review • The Simulation Framework • Simulation Results • Conclusion

  23. Conclusion • Ignoring the existing dependency structure between mortality rates and macroeconomic changes leads the insurer to systematically underestimate true insolvency probabilities • The relative increase in insolvency probability is higher for insurers with: • relatively mature insureds • large portfolios • a high stock exposure • a high amount of equity capital

  24. Conclusion • The interaction between mortality and macroeconomic conditions needs to be an integral part of • life insurers’ internal risk models • capital allocation decision making • of solvency assessment by rating agencies and regulatory authorities • This will lead to • more accurate assessments of an insurer’s risk situation • more effective protection of policyholders’ interests

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