Reinsurance and securitization: Application to life risk management. Pauline Barrieu Henri Loubergé

Transcription

1 securitization: Application to life risk anageent Pauline Barrieu Henri Loubergé

2 2 Background Traditional reinsurance theory (Borch, 1960, 1962): a reinsurance pool is fored to share undiversifiable risk; reinsurers are EU axiizers; they share risk according to their risk-tolerance (Wilson, 1968); risk-sharing is copleted by bargaining on side-payents to allocate gains fro diversification ( theory of gaes). Over the past 20 years the reinsurance industry was confronted with huge systeatic risks... Insurance-Linked Securities (ILS) where created to get financial investors involved in the world-wide sharing of risks (see, e.g., cat bonds).

3 3 Paper Motivation Use the theory of risk easures to provide a general theory of risk-sharing aong three representative agents: insurer reinsurer investor Apply the theory to a challenging social risk faced by insurers today: longevity risk. Investigate the ipact of conteplated regulatory easures on risk-sharing.

4 4 Longevity risk Long-ter trend of longevity increases globally, ore particularly in developed countries. Uncertainty about the future (changes in trends? jups? or liits to longevity?). Already treendous ipact on pensions (pay-as-you-go systes as well as funded systes) delay of andatory retireent age. switch fro defined benefit to defined contribution. Challenge also for insurers: undiversifiable risk with positive ipact on death insurance (if death probability overestiated); negative ipact on life insurance (annuities).

5 5 Increase in life expectancy in the USA (Source: Boucher and Boyer, 2009) Period Total change Origin by age less than 1 year 30% 22% 24% 1 to 14 28% 11% 6% 15 to 44 23% 25% 6% 45 to 64 6% 17% 27% 65 and ore 3% 19% 35% Multi-generation 11% 6% 2%

6 6 Life expectancy of en at 65 (Source: Boucher and Boyer, 2009) Country Change Gerany UK Australia Canada USA Finland France Japan

7 7 Life expectancy (2) Longevity tables display a systeatic trend. The trend was underestiated in the past. Will it continue at a steady pace or not? Moreover, longevity risk has also a specific coponent: average longevity varies across insured populations. This risk is diversifiable using reinsurance. The systeatic coponent ust however be assued by the insurance industry or shared with financial investors. 3-agent odel

8 8 Three agents Insurer faces a ortality rate with a systeatic and a specific coponent. Pays a stochastic aount: ˆ X = X ( Θ ) + X ( Θ ) einsurer supplies coverage to an aount Ĵ at price κ and issues a ortality bond with a contingent payoff M ( Θ) at price π. Financial investor pays π to get the contingent payoff M ( Θ)

9 9 Decision criterion Monetary risk easure ρ (Ψ) with desirable coherence properties (Föller and Schied, 2002): positive hoogeneity convexity (leading to sub-additivity). A risk easure represents a onetary aount which should be put on reserve to copensate for the risk (analogy with Va). Modified risk easure ρ (Ψ) using a change of probability fro P to Q to reflect optial financial investent on the arket (Barrieu-El Karoui, 2003).

10 10 Assuptions Use of entropic (odified) risk easure to perfor iniizations: 1 ρa ( Ψ ) = γ a ln E ˆ exp( ) Q Ψ γ a Link with EU: the entropic risk easure is the opposite of the certainty equivalent of the risk for negative exponential CAA utility: ρ(x) = - C x. The reinsurer organizes transfers and iniizes his risk easure under constraints of no increased risk for the insurer and the investor.

11 11 Proble General forulation: in ρ ( W Jˆ M ( Θ ) + π + κ ) Jˆ, M s.t. ( ˆ ˆ ρ W X + J κ ) ρ ( W Xˆ ) I I I I ρ ( W + M ( Θ) π ) ρ ( W ) B B B B Using the cash invariance property of risk easures: in Jˆ, M { ( ˆ ( )) ( ˆ ˆ ) ρ ( ( )) } W J M Θ + ρi WI X + J + ρb WB + M Θ

12 12 Proposition 1 : Optial contracts Optial risk-sharing of specific risk: * γ J ( Θ ) = X ( Θ ) + constant γ + γ Optial risk-sharing of systeatic risk: J M * * I γ + γ B ( Θ ) = X ( Θ ) + constant γ + γ + γ I B γ B ( Θ ) = X ( Θ ) + constant γ + γ + γ I B

13 13 Transaction feasibility Let π B represent the axiu buying price for the bond. Let π represent the iniu selling price of the reinsurer for the bond. Proposition 2: π B - π > 0.

14 14 egulatory constraints Threat of increased regulatory constraints on insurance/reinsurance activity in the afterath of the subprie crisis and AIG failure. More stringent reserve requireents (inflated risk easures), with Solvency II. Possible penalty on securitization activity for reserve requireents purpose. Possible iniu risk-retention requireents for insurers and reinsurers issuing ILS. Two possible regulations considered in the paper.

15 15 Case 1: Different reserve requireents on securitization The iniization progra is now: ( ˆ in ρ W J + κ) + αρ ( M ( Θ ) + π ) Jˆ, M s.t. ( ˆ ˆ ρ W X + J κ) ρ ( W Xˆ ) I I I I ρ ( W + M ( Θ) π ) ρ ( W ) B B B B Due to separation between insurance risk-sharing and securitization, the optial contracts are now: ˆ* γ J = Xˆ M * ( Θ ) = 0 γ γ + I The rationale for securitization disappears and reinsurance capacity is reduced.

16 16 Case 2 : Penalty on securitization ILS are now inflated (or deflated) by a factor α for risk anageent purposes. The iniization proble is now: in ρ ( W Jˆ + κ + α M ( Θ ) + π ) Jˆ, M With results: [ ] s.t. ( ˆ ˆ ρ W X + J κ ) ρ ( W Xˆ ) I I I I ρ ( W + M ( Θ) π ) ρ ( W ) B B B B * γ J ( Θ ) = X ( Θ ) + constant γ + γ I

17 17 Case 2 (cont d) J M * * γ ( γ + αγ B ) ( Θ ) = X ( Θ ) + constant γ ( γ + αγ ) + γ ( γ + ( α 1) γ ) B I B γ Bγ ( Θ ) = X ( Θ ) + constant γ ( γ + αγ ) + γ ( γ + ( α 1) γ ) B I B Proposition 6: J * and M * are increasing in α. In this case, iposing α > 1 (α < 1 ) on securitization reporting will increase (decrease) securitization and reinsurance transfers.

18 18 Conclusions Two ain conclusions. 1. isk iniization leads to dual risk anageent: traditional risk-sharing of specific risk between insurers and reinsurers; risk-sharing of systeatic risk between insurers, reinsurers and financial investors. 2. Strong sensitivity of systeatic risk transfer to regulation on securitization activity. Depending on the kind of restrictions iposed on ILS underwriting, reinsurance capacity ay be boosted, reduced or brought to zero.