P ARTIAL S PLITTING OF L ONGEVITY AND F INANCIAL R ISKS : T HE L IFE - PowerPoint PPT Presentation

Interest rate risk transfer Mortality and longevity modeling Quantative analysis P ARTIAL S PLITTING OF L ONGEVITY AND F INANCIAL R ISKS : T HE L IFE N OMINAL C HOOSING S WAPTIONS H. Bensusan (Société Générale) joint work with N. El Karoui, S. Loisel and Y. Salhi Longevity and Pension Funds February 4th, 2011 Thanks to C. Michel and all the R & D team of CACIB H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis O UTLINE OF THE TALK 1 I NTEREST RATE RISK TRANSFER 2 M ORTALITY AND LONGEVITY MODELING 3 Q UANTATIVE ANALYSIS H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis I NTRODUCTION ◮ Improvements in longevity are bringing new issues and challenges at various levels: social, political, economic and regulatory. ◮ Need of MORE AND MORE CAPITAL to face this long-term risk ◮ Hedging longevity risk is now an important element of risk management for many organisations H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis L ONGEVITY R ISK : R ISK M ANAGEMENT S UBJECT FOR I NSURANCE COMPAGNIES The insurance industry is also facing some specific challenges related to longevity risk. ◮ Accurate longevity projections are delicate (prospective life tables) ◮ Modeling the embedded risk (such long term interest rate risk) remains challenging ◮ Important to find a suitable and efficient way to cross-hedge or to transfer part of the longevity risk to reinsurers or to financial markets H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis H ETEROGENEITY ◮ Longevity patterns and longevity improvements are very different for different countries, and different geographic area. ◮ Factors affecting the mortality socio-economic level (occupation, income, education...) gender marital status living environment (pollution, nutritional standards, hygienic...) wealth H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis B ASIS RISK I Difference between the national mortality data and the one from an insured portfolio. ◮ Insurance companies have much more detailed information They know the exact ages at death and not only the year of death (time continuous data) Cause of death are specified Characteristics of the policyholders : socio economic level, living conditions ... ◮ BUT limited size of their portfolios (in comparison to national populations : 700 000 individuals from 19 different insurance companies) small range of the observation period Furthermore, insurers are tending to select individuals (given their health and medical history for example). This heterogeneity is very important for longevity risk transfer based on NATIONAL INDICES : for too important basis risk, the hedge would be too imperfect H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis O UTLINE 1 I NTEREST RATE RISK TRANSFER 2 M ORTALITY AND LONGEVITY MODELING 3 Q UANTATIVE ANALYSIS H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis F INANCIAL RISK TRANSFER Insurance companies are exposed to interest rate risk ◮ Annuities at rate k ◮ Investments in interest rate products (Bonds,...) Looking for a product that transfers interest rate risk while keeping longevity risk: ◮ Insurance can manage longevity risk ◮ Banks can manage intereste rate risk ⇒ Product with decorrelation of both risks H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis Y ES BUT HOW ? Difficulties for launching a pure longevity product: ◮ No longevity market (No shared reference) ◮ Information asymmetry ◮ Modelling and pricing (evaluation in historical probability) ⇒ Pure interest rate products H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis R EAL PORTFOLIO F IGURE : Age distribution of policyholders H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis P ORTFOLIO EVOLUTION F IGURE : Survival extreme scenarii of policyholders Using our longevity model H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis C HALLENGES Interest rate hedging of life-insurance products : ◮ Static hedge of interest rate risk ⇒ Swaps ◮ Dynamic hedge of forward risk ⇒ Swaptions ◮ Longevity ⇒ Swaptions with variable nominal ◮ Stochastic evolution of longevity ⇒ Choice of the nominal profile H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis L IFE N OMINAL C HOOSING S WAPTION ◮ Swaption on a swap with variable nominal N t with strike k : � N � P swaption ( k − SV T ( T 0 , T N , δ, N t )) + � E Q T = B ( T , T i ) N T i δ B ( 0 , T ) i = 1 ◮ Choice of α T ∈ [ 0 , 1 ] by the insurer at date T (with available information) ⇒ Hedge on the nominal series N α T + ( 1 − α T ) N + = α T N − t t t t , N + ◮ Forward swap rate with variable nominal SV T ( T 0 , T N , δ, α T , N − t ) for the series N t determined by α T ◮ Evaluation of "Life Nominal Choosing Swaption" (LNCS) at strike k :     N P LNCS E QT   ( k − SV T ( T 0 , T N , δ, α T , N − , N + )) + B ( T , T i )( α T N −  � Ti + ( 1 − α T ) N + = Ti ) max   δ B ( 0 , T ) 0 ≤ α T ≤ 1  i = 1     N l l l   E QT , N − , N + )) + � N − ) N +  max  ( k − SV T ( T 0 , T N , δ, B ( T , T i )( Ti + ( 1 − Ti ) ∼  0 ≤ l ≤ n n n n  i = 1 H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis C HOICE OF α T ( EXAMPLE ) F IGURE : Choice of the parameter α T in 2019 Using our longevity model H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Hedging of life-insurance products Quantative analysis C HOICE OF α T ( EXAMPLE ) F IGURE : Choice of the parameter α T in 2029 Using our longevity model H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis O UTLINE 1 I NTEREST RATE RISK TRANSFER 2 M ORTALITY AND LONGEVITY MODELING 3 Q UANTATIVE ANALYSIS H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis C AIRNS , B LAKE AND D OWD (CBD) M ODEL (2006) The 2-factor CBD model gives the dynamics of the annual mortality rate q t ( x ) at age x during the year t : logit q t ( x ) = A 1 ( t ) + xA 2 ( t ) . � � x where the function logit is defined by logit ( x ) = ln . 1 − x H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis I NDIVIDUAL MORTALITY MODEL AIM: Reduce the basis risk by estimating the deviation of the "individual mortality" from the average mortality (as given by mortality tables). ◮ Find individual characteristics (such as socio-economic level or income) that can explain mortality ◮ Take them into account in a stochastic mortality model The mortality model by age and trait (feature) is calibrated on national mortality data and on specific data (i.e. with information on individual characteristics) H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis M ARITAL STATUS INFLUENCE AT INITIAL DATE (M ALES ) F IGURE : Logit of mortality rate for French males in 2007 with different marital status H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions

Interest rate risk transfer Mortality and longevity modeling Quantative analysis M ORTALITY PROJECTIONS IN 2017 (M ALES ) F IGURE : Logit of mortality rate for French males in 2017 with different marital status H. Bensusan (Société Générale) The Life Nominal Choosing Swaptions