Roles for Financial Engineering In the Life Insurance Industry

4,648 views

Published on

2006 Quant Congress USA

Published in: Economy & Finance, Business
4 Comments
7 Likes
Statistics
Notes
No Downloads
Views
Total views
4,648
On SlideShare
0
From Embeds
0
Number of Embeds
311
Actions
Shares
0
Downloads
0
Comments
4
Likes
7
Embeds 0
No embeds

No notes for slide

Roles for Financial Engineering In the Life Insurance Industry

  1. 1. Roles for Financial Engineering In the Life Insurance Industry Quant Congress USA New York, July 13th 2006 Frank Zhang, FSA, MSCF, CFA, FRM, PRM Senior Quantitative Derivatives Strategist Head of Quantitative Financial Modeling & Hedging ING USFS Annuity Market Risk Management Frank.Zhang@US.ING.Com 610-425-4222 1
  2. 2. Executive Summary Life insurance products are increasingly derivatives oriented and many of the same derivatives valuation techniques apply The hybrid products also create unique challenges and opportunities to financial engineers and derivative markets 2
  3. 3. Agenda Innovations and exotic derivatives sold as life insurance contracts Challenges facing financial engineers in the life insurance industry Quantitative research and stochastic model development opportunities 3 Ask Questions
  4. 4. Life Insurance or Derivatives? Guarantees blur the boundary between derivatives products and traditional life insurance products Living or dying! Variable Life Life Derivatives Derivatives Insurance Insurance Annuities Diversifiable Non-diversifiable Law of large numbers Derivatives pricing Mutual Mutual Funds Funds Multiple underlying assets All VA contracts invest in mutual funds, paying fees to insurer, and getting guarantee benefits GMDB (Guaranteed Minimum Death Benefit) => Payable at death VAGLB (Variable Annuity Guaranteed Living Benefit) => Payable Under Predefined Condition: GMAB (Guaranteed Minimum Accumulation Benefit) for account value guarantee GMIB (Guaranteed Minimum Income Benefit) for annuitized payouts guarantee GMWB (Guaranteed Minimum Withdrawal Benefit) for withdrawals guarantee 4
  5. 5. Variable Annuity Contracts Guarantees & Fees Guarantee payoffs = f( total basket value of mutual funds) Account Value (AV) = total of underlying basket of assets. Contracts may be subject to surrender charge (SC) if lapsed during initial 8-12 years. Contract pays AV-SC but no GMDB/VAGLB benefits if voluntarily surrendered. Strikes of guarantees can take many different forms. Partial withdrawals are allowed, but the strikes are reduced accordingly. Contract pays insurer and mutual fund manager fees over time Surrendering the contract is an option to stop paying the fees. Fees maybe based on strikes (less costly for option writer) or on asset values. Not everyone exercises the option optimally!? Policyholder may not be able to easily identify the optimal exercising strategy. Wide difference between savvy and naïve. Need to aggregate individual specific behavior rather than use average behavior. 5
  6. 6. Variable Annuity: GMDB Guarantees GMDB – benefits are put options paid upon death A form of life insurance but structured as derivatives Claims = max (0, GMDB –AV) x mortality Option premium paid as ongoing fees Example of a max 6% GMDB If owner dies at time t, the payoff is AVt+max(0,Striket-AVt) Strike0 = AV0 Strikek = max(Strikek-1, AVk, AV0*1.06k), k=1,2,3,… The ratcheting (lookback) feature can become very costly in bull market scenario The worst case scenario is death after a market crash 6
  7. 7. Variable Annuity: GMDB Designs Different strikes for different designs Return of premium: strike = initial AV = initial premium deposits Ratchet: discrete look back strike = max (sample AVs during the contract life) Rollup: increasing strikes at an annual rate x: strike t = (1+x)t Combinations: strike = max of ratchet and rollup 7
  8. 8. GMDB Derivatives Pricing Claims = max (0, GMDB –AV) x mortality Least subject to policyholder behavior Most people don’t choose to die to get paid for the guarantee (relatively small) Based on law of large numbers, the mortality can be estimated quite accurately GMDB price: f=ΣkPkPV(Payoffk) or f= ΣkPkPV(Payoffk-feesk) Pk = probability of surviving to the beginning and then die during the period k Each period payoff can be priced as if it is a standard put option GMDB is priced a series of put options, contingent on death 8
  9. 9. GMDB Pricing Benefit Paid Upon Death Death benefit paid upon death Rate of mortality based on law of large numbers Mortality rates increase quickly at older ages 9
  10. 10. GMDB Pricing Benefit Paid Only If GMDB Contract Is Still In Force At Death Not all contracts initially issued still in force in later years People could lapse the contract or annuitize (decrements) 10
  11. 11. GMDB Pricing Putting All Pieces Together GMDB is paid only If GMDB is in the money and still In force at death Price = sum of all future possible death payoffs on persist contracts 11
  12. 12. A GMWB Example GMWB is a rider Pay additional fees Based contract has also GMDB 7% Withdrawal guarantee Maximum 7% of AV0 withdrawal per year Guaranteed to get AV0 Likely scenario to pay off Bear market & rapid draw down in early years Allows no time for recovery Richer benefits still Reset to higher account value with or without limit If there is no withdrawal after 5 years, the benefit base may be stepped up 20% 12
  13. 13. GMWB Derivatives Pricing Claims = max (0, PV of guaranteed future withdrawals –AV) x persistency GMWB price: f= ΣkPkPV(Payoffk) or f= ΣkPkPV(Payoffk-feesk) Pk = probability of surviving to the period k (persistency) GMWB starts to pay off once AV=0 but total withdrawals < guaranteed Critically a function of policyholder behavior Path dependent based on ITM/OTM, reset features, etc. Law of large numbers is barely enough Very little experience exists Withdrawal utilization is a big assumption for GMWB pricing Typically priced using simulations Underlying assets may still be the freely reallocated mutual funds Assumption of withdrawal behavior can result in very different prices M.A. Milevsky, T.S. Salisbury / Insurance: Mathematics and Economics 38 (2006) 13
  14. 14. Costly GMWB in Bear Markets 14
  15. 15. Costly GMWB Reset in Bull Market 15
  16. 16. GMWB Pricing Putting All Pieces Together GMWB is paid only If GMWB is in the money and still In force when AV=0 Persistency and payoff amounts are path dependent Price = sum of all future possible GMWB payoffs on persist contracts 16
  17. 17. 17
  18. 18. GMWB Risks Key Elements Details Exposure to implied volatility, rates, and market paths Market Risks Significant exposure to positive (calls), as well as Reset Risk negative (puts), market performance Large Gammas Significant systematic risks – originally diversified Calendar Reset Risk portfolio from different periods of issues and different investment experience will all start at the money after reset Will client stay on when “in the money”? Persistency Risk Investment in higher volatility funds more costly Asset Allocation Risk How many will take the WB and how do they respond to Elections Risk ITM The shorter term creates more volatility risks than No Waiting Period income benefits, because policyholders can withdraw money at anytime without waiting 18
  19. 19. Agenda Innovations and exotic derivatives sold as life insurance contracts Challenges facing financial engineers in the life insurance industry Quantitative research and stochastic model development opportunities 19 Ask Questions
  20. 20. What Makes These Annuities Challenging? Annuity derivatives pricing • Simulations often the only choice • Dynamic policyholder behavior modeling critical but unreliable • Underlying mutual fund assets not directly tradable • Long term contracts difficult to price Long term hedging strategy projections • There is something better than back testing • Constructing nested stochastic on stochastic simulations • Garbage in and garbage out 20
  21. 21. Annuity Derivatives Pricing Challenges Stochastic Simulations Simulations often the only choice • No closed form solutions • Path dependency • Amortizing options • Multiple underlying assets • Very complex rules • Individual modeling • Option premiums (fees) collected over time Lack of useful research • Most existing theoretic researches can’t deal with path dependency • Passport optionality • American optionality • Faster lattice approach rarely used 21
  22. 22. 22
  23. 23. Annuity Derivatives Pricing Challenges Dynamic Policyholder Behavior Modeling – Critical and Difficult Dynamic policyholder behavior modeling is critical • Key driver for pricing • Options not always exercised optimally • Historically don’t always keep contracts to maturity due to death or lapse • Capital market risks don’t diversify Dynamic policyholder behavior modeling is difficult • Mortality risk managed by pool of large numbers • Living benefits much more challenging • Behavior very difficult to predict • Freely asset reallocation • Little or no experience • Policyholder dynamics causing significant gamma exposure 23
  24. 24. Annuity Derivatives Pricing Challenges Blend of Actuarial Science and Financial Engineering • Actuarial decrements (deaths and lapses) a new dimension to standard derivatives • Annuity derivatives pricing unique due to dynamic policyholder behavior • Actuarial risks unhedgable by the existing capital market instruments • Contracts tend to be very long term There are significant residual Policyholder behavior risk risk not tradable so managed on an actuarial basis. Variable Annuity Guarantee • Need to link financial and Pricing and Hedging actuarial valuation • Dynamic “recalibration” of hedge strategy and model • Determining a good hedge assumptions using structure requires deep rigorous performance understanding of the attribution Actuarial benefits Science • Manage to static, expected • Hedge strategy is unique behavior but be ready for every time with new the worst-case behavior. experience Financial • Develop and fine tune a Engineering • Careful design and market-linked policyholder marketing carries rewards behavior function. 24
  25. 25. 25
  26. 26. Annuity Derivatives Pricing Challenges Comparison: Variable Annuities • Variable annuities are sold to individual investors who pay money to insurance company. • VAs pass through mutual fund performance BUT add derivatives guarantees • There is no active secondary market who collect the investments from the investors 26
  27. 27. Annuity Derivatives Pricing Challenges Comparison: Mortgages • Mortgages are sold to banks/institutional investors who pay money to fund houses. • The funding needs created secondary MBS markets • MBS are created to pool mortgages. 27
  28. 28. 28
  29. 29. Annuity Derivatives Pricing Challenges Dynamic Policyholder Behavior Modeling – Lessons Learnt from MBS? Dynamic policyholder behavior vs. MBS prepayments • Behaviors heterogeneous vs. aggregation • Non-linearity • In-the-moneyness • Smaller contracts • Reset is similar to refinancing • Unlike MBS, there is no market to trade the annuity contracts yet • Annuity contract too small and owned by individuals, unlike mortgage pools • No active market to verify the annuity prices and the “prepayment” models Betting on policyholder inefficiency a dangerous proposition • Increasingly efficient behavior • Increased awareness • Convergence with capital markets pricing • Hedge fund for most aggressive asset allocations and more use of withdrawals 29
  30. 30. Annuity Derivatives Pricing Challenges Multiple Underlying Mutual Fund Assets – Tradability Underlying mutual fund assets not directly tradable Assets invested in equity and bond mutual Each contract is different and needs to be modeled funds of variety of investment styles separately Making the fund performance history less reliable for Fund managers actively manage their portfolios future hedging (with minimum variance hedging by and may change the investment styles multiple regression analysis) Making the derivatives valuations less precise since Contract owners may actively reallocate their the contract assets can not be locked in during funds freely – Passport optionality valuation There are usually not directly corresponding tradable liquid index instruments or ETFs for Making static replication less than ideal variable annuities The underlying funds often can’t be sold short Shorting usually based on index futures or options by the insurance company Portfolio management fees and insurance fees deducted (total about 2-4% a year) from the Causing a downward bias to account value contracts 30
  31. 31. Annuity Derivatives Pricing Challenges Multiple Underlying Assets – Basic Risks, Model Risks and Mitigations Basis risks and tracking errors • Most derivatives research assume simplified asset classes • Very little attention on regression based minimum variance hedging and its tracking errors Model risks • Not accurate in small changes in market (Delta) • Not accurate for jumps in market (Gamma) • Not accurate for changes in price of hedge (Vega) • Not accurate for changes in interest rates (Rho) • Not accurate for changes in actuarial assumptions (dynamic policyholder behavior risk) Mitigation • Asset allocation restrictions • Pool of large assets that are more like the market portfolio • Proper design of the benefits 31
  32. 32. Annuity Derivatives Pricing Challenges Very Long Term Contract Durations Long term contracts difficult to price • Very thin market for longer term options (30+ years) • Significant interest rate risks • Supplies and demands often disrupt the patterns volatility curves • Very little reliable data available • Hybrid of equity and interest rate products significant correlation risks • Correlation a 2nd order risk with 1st order pricing implications • Perfect hedges break down due to correlations Long term projection of capital market parameters • Annuities priced to the models, not to the markets • Pricing models for traditional derivatives too simplified for annuity pricing • Push the theoretical boundary to model equity, interest rates, and volatilities • Long term arbitrage free modeling important but not yet available • Integrated equity volatility and interest term structure volatilities 32
  33. 33. What Makes These Annuities Challenging? Annuity derivatives pricing • Simulations often the only choice • Dynamic policyholder behavior modeling critical but unreliable • Underlying mutual fund assets not directly tradable • Long term contracts difficult to price Long term hedging strategy projections • There is something better than back testing (alone) • Constructing nested stochastic on stochastic simulations • Garbage in and garbage out 33
  34. 34. Long Term Financial and Hedging Projections There is something better than back testing (alone) For projecting VaR and economic capital Stochastic-on-stochastic into the future and testing different real world and risk techniques for efficient financial and neutral projections capital managements under different accounting rules and capital rules Long term financial projections are core of actuarial technology Required for regulatory “Realistic” projections of capital and reserve the future more dynamic CTE calculations and comprehensive than simple back testing or stress testing To test optimized hedge Calculate option values and strategies and derivatives Greeks along the paths of real positions under different world financial projections market scenarios 34
  35. 35. 35
  36. 36. 36
  37. 37. 37
  38. 38. 38
  39. 39. 39
  40. 40. 40
  41. 41. Long Term Financial and Hedging Projections Scenarios Need to project market assumptions many years into the future • Scenarios are the key to long term projection analysis • Garbage in and garbage out • Real world and risk neutral world consistent with each other • Much more than back-testing or scenario testing • Very little research for long term integrated scenarios available Market levels, interest rate curves, implied volatility surfaces, correlations, and dividend yields Need realistic model of joint distributions • It is not easy to form a long term expectations of volatilities Short-term ATM implied volatility reflects recently realized volatility Longer-term ATM implied volatility depends on supply/demand for long-term options • Interactions and correlations of different assets for both equity and fixed income securities 41
  42. 42. Agenda Innovations and exotic derivatives sold as life insurance contracts Challenges facing financial engineers in the life insurance industry Quantitative research and stochastic model development opportunities 42 Ask Questions
  43. 43. Research Opportunities Numeric Simulations – General Directions Annuities are path-dependent, multivariate, and amortizing options and brute-force simulations are too slow Many derivatives formulas from researches don’t apply to multiple underlying assets. Need more effective numerical valuation techniques • Traditional variance reduction techniques (importance sampling, antithetic or control variates, LDS). – Antithetic variates don’t work well for deep out-of-the-money options, for reset features, nor for tail measures. – Importance sampling does not work well for net liabilities (claims net of the offsetting fees) because of path dependency and different timing of cash flows – Low discrepancy sequences lose advantage in the high dimensional problems here. More research combining the traditional MCS with LDS is ongoing and promising • Closed form solutions under simplified assumptions may not provide direct price but can aid understanding and may be for control variates 43
  44. 44. Research Opportunities Numeric Simulations – General Ideas Numerical simulation techniques • Scenario cache or reuse – memory search & lookup and latency issues vs. generating the scenarios • Redesign the simulation structure to optimize the calculations and speed up the computations • Research and simulation test trade-offs between speed and hedging effectiveness with and without the cross-Gammas and other high order or cross Greeks • Scenario reduction with efficient use of random numbers vs. the number of instruments • Brownian bridge method to reduce bias in ratchet options • Application PCA methodology to modeling and hedging when using term structures of interest rates and volatilities 44
  45. 45. Research Opportunities Some Recent Numeric Simulation or Hedging Techniques Credit: Discussions here are based on a March 2006 presentation by Richard C. Payne, Genesis Financial Products Inc. Orthogonal polynomial variance reduction (Chorin): – Expanding the option payoffs function in a series of weighted orthogonal polynomials – Weights come from density of index at the payoff date – Hermite polynomials, orthogonal with respect to integration over normal distribution Multivariate discrete lookback (high water mark): Laplace transforms, lattice rules, PDE finite difference methods, continuity corrections to continuous lookbacks, convolution, Fast Fourier Transforms Scenario hedging: matching without using Greeks but using reasonable set of possible assets – Find mix that stays “close” over “most” scenarios using linear programming – Start with certain # of scenarios (say 100) and move ahead to retest 45
  46. 46. An Interesting Sample Research Decomposition using Linear Path Space (LPS) by Ho and Mudavanhu The path space is a representation of all the possible scenarios The recombining lattice offers a “coordinate system” to represent the possible scenarios Structured sampling of the path space provides equivalent classes of possible scenarios, and the lattice framework enables us to measure the size of the classes 46
  47. 47. Decomposition using Linear Path Space (LPS) References Ho, Lee and Choi: “Practical Considerations in Managing Variable Annuities” Working Paper 2006 Ho and Mudavanhu: “Decomposing and Managing Multivariate Risks: the Case of Variable Annuities” Journal of Investment Management 2005 Ho and Mudavanhu “Managing Stochastic Volatility Risk of Interest Rate Options: Key Rate Vega” working paper 2006 Papers available at www.thomasho.com 47
  48. 48. Research Opportunities Long Term Financial Projections – Economic Models Integrated long term economic models • Integrated equity, interest, and volatility scenarios • Arbitrage free and realistic • Implied volatility, realized volatility, and correlations • Very long term • Easy to implement • Consistency between risk neutral and real world Examples • Long term stochastic volatility modeling • Long term interest rate term structure modeling • Regime switching process modeling • NA-GARCH=Nonlinear Asymmetric Generalized Autoregressive Conditional Heteroscedasticity. J.C. Duan, The GARCH Option Pricing Model, Mathematical Finance, 1995 48
  49. 49. An Interesting Sample Research for Long Term Projections Efficient Stochastic Modeling with Representative Scenarios What is representative scenario methodology? • A variance reduction procedure to reduces the number of scenarios needed to apply stochastic financial projection cash flow models • Developed by Longley-Cook (1997, 2003) and Chueh (2002) Central to this methodology is the notion of distance (D) between scenarios Actuarial knowledge of the relationship between scenarios and cash flows is used to efficiently select representative scenarios Representative scenarios reduce run-time by reducing the number of scenarios but results are often very similar to those using all scenarios Very effective in sampling tail distributions 49
  50. 50. Efficient Stochastic Modeling with Representative Scenarios Choose the representative scenarios 50 (n) representative scenarios were selected using algorithms described in Chueh’s paper (2002) Relative present value distance method * S refers to the significance of a scenario, as defined by Chueh(2002), and is used in a slightly different method in which each representative scenario has an equal probability of occurrence 50
  51. 51. Efficient Stochastic Modeling with Representative Scenarios References Longley-Cook, Alastair G., “Efficient Stochastic Modeling Utilizing Representative Scenarios: Application to Equity Risks”, presented at CIA 2003 Toronto Stochastic Modeling Symposium Chueh, Yvonne, “Efficient Stochastic Modeling for Large and Consolidated Insurance Business: Interest Rate Sampling Algorithms,” North American Actuarial Journal, Volume 6, Number 3, July 2002 Hardy, Mary R., “A Regime-Switching Model of Long-Term Stock Returns,” North American Actuarial Journal, Volume 5, Number 2, April 2001 Joy, Corwin; Boyle, Phelim P.; Seng Tan, Ken, “Quasi-Monte Carlo Methods in Numerical Finance,” Society of Actuaries Monograph, Investment Section Abstract (July 2002) Longley-Cook, Alastair G., “Probabilities of ‘Required 7’ Scenarios (and a Few More),” The Financial Reporter (July 1997) 51
  52. 52. More Research Opportunities Dynamic Policyholder Modeling Advanced and efficient modeling of dynamic policyholder modeling • Blending financial engineering with actuarial science • MBS prepayment lessons • Realistic pricing of VAGLB derivatives assuming path-dependency • Need to test optimal exercise at least approximately using Tilly’s path- bundling techniques. J.A. Tilly, Valuing American Options in a Path Simulation Model, Transactions of Society of Actuaries, 1993 • Other pricing methodology (in addition to simulations) for path-dependent derivatives • Windcliff, et. Al., “Understanding the Behavior and Hedging of Segregated Funds Offering the Reset Feature”, North American Actuarial Journal 6(2) 52
  53. 53. More Research Opportunities Hedging Performance Attribution Dynamic hedging performance attribution • Very important for practical applications but researches in this areas are limited • Basis risk and tracking errors • Discrete trading • Non-constant volatilities • Correlations: since rates and volatilities can be easily hedged in the market, correlation is often the dominate risk in many trades 53
  54. 54. Research Opportunities Integrated Interest Rates and Volatilities Valuing EIA and VA when interest rates and volatilities are stochastic • Traditional pricing using static interest rates or volatilities is no longer appropriate • Longer maturity create more model risks • Need to consider both stochastic interest rates and volatilities • Testing the hedging strategies and capital requirements over long horizon under the real world measure requires models to work under both the risk neutral and real world measures • Learning from convertibles, hybrid and structured products? • Fung and Li, “Valuation of Equity-Indexed Annuities when Interest Rates are Stochastic”, Working paper (2006) • Lin and Tan, “Valuation of Equity-Indexed Annuities under Stochastic Interest Rates”, North American Actuarial Journal 7(4) 54
  55. 55. Your Questions & Comments The future of integrated financial engineering and actuarial science is here
  56. 56. Appendices More discussions on VA and EIA benefits Advanced Computing technology challenges Complex accounting and profitability challenges Improve the hedging with adaptive learning 56
  57. 57. Appendix 1 More Discussions on VA and EIA Products • Comparison of Living Benefits (VAGLB) • GMAB • GMIB • EIA • Comparison of EIAs and VAs • Examples of dynamic policyholder behavior modeling 57
  58. 58. Variable Annuity Contracts Living Benefits Comparisons 58
  59. 59. A GMAB Example with Pricing Example of a variable annuity contract with GMAB • GMAB is usually a rider on the base contract with GMDB already • Contract guarantees the maturity value after, for example,10 years is the return of premium (initial deposit) no matter how the account performs • Simplest VAGLB and closed to standard put option • Policyholders are most likely to exercise the option optimally but still need to model dynamically – path dependent Derivatives Pricing for GMAB • Claims = max (0, GMAB –AV) x surviving probability to the end of year 10 • GMAB price: f=p10PV(payoff10) • Pk = probability of surviving to the end of the waiting period • Pk is still not 100% because of some non-optimal lapse behavior and some people die before the waiting period • The payoff is like a standard put option but path dependent 59
  60. 60. GMIB Summary Typically, GMIB typically allows the income benefit of a variable annuity to increase at the greater of a) the market value, b) some fixed roll up rate and c) the policies annual or quarterly anniversary high watermark. • Features a) and c) above are essentially the same as in most GMDB policies. Feature b) add an additionally fixed income floor to the policies’ income value Generally, the GMIB value will only count toward annuitization – and then only at terms that are generally unfavorable • For example, a policy might be worth $200,000 and have a GMIB value of $250,000. However, annuitizing the $200,000 at market rates could produce a higher annual payout than annuitizing the $250,000 GMIB amount given the terms imbedded in the GMIB policy • Annual election only during 30 days following anniversary to diversify benefit election risks • However, if rates are low, especially in the Japan scenario, the differences between annuitization rates generally collapse. So a GMIB is most likely to be exercised if rates are low GMIB is subject to the annuitization decision – after a waiting period. This decision will, generally, only utilize the GMIB feature in low rate environments. • The worst scenario is good equity performance in early years, setting guarantees at high levels (effect of annual or quarterly ratchet). Then followed by severe bear market, compounded with declining and low interest rates 60
  61. 61. A GMIB Example Example of a variable annuity contract with 6% GMIB • GMIB is usually a rider on the base contract with GMDB already • Contract guarantees the maturity value after, for example,10 years waiting • NAR = max (0, Factor x PV of guaranteed annuity income from GMAB – AV) • Factor10 = Strike10/ Strike0 Strike0 = AV0, and Strikek = max(Strikek-1, AVk, AV0*1.06k), k=1,2,3,… • • Claims = NAR x annuitization utilization % for each of the years after the waiting period • Annuitization utilization is a huge unknown, almost no experience (still in waiting) • The ratcheting (lookback) feature can become very costly in bull market scenario • The rollup (6% in this example) also significantly increase the cost • The only catch is that PV of guaranteed annuity income from GMAB / AV10 <1 if – The interest rate in the future is higher than the guaranteed rate of 1-3% and – The longevity rate in the future is not higher than guaranteed rates in the contract 61
  62. 62. Costly GMIB in Bull Market 62
  63. 63. GMIB Derivatives Pricing The guarantee is an equity put option sold by the insurer, where the strike is a bond, subject to the interest rate risks Need equity/interest rate model • One example of a 2-factor interest rate model – Recombining lattice, orthogonal yield curve movements – Fit the term structure of interest rates and volatilities (arbitrage free) • Combining lognormal an normal behavior – Equity returns are lognormal – The instantaneous rate of return = short rate • GMIB may be represented as a portfolio of equity options and bond options GMIB price: f= ΣkPkPV(Payoffk) or f= ΣkPkPV(Payoffk-feesk) Pk = probability of surviving to the beginning of the period k and then annuitize during the period k The path-dependent derivatives can be priced with time consuming stochastic multivariate simulations Path-dependency is caused by dynamic policyholder behavior in lapses, partial withdrawal, and annuitization 63
  64. 64. Indexed Annuity Contracts Fixed Annuity • Supported by general account assets (mostly fixed income and thus fixed annuities) and call options • With minimum annual return guarantee of 1-3% to protect against loss of principal “Interest” credited periodically like fixed annuities or CDs but based on some predefined equity performance • Term point to point/term high water mark/Annual reset point to point/annual reset monthly average (Asian)/monthly sum cap Similar to interest rate notes with equity participation payoffs Generally Asian with discrete look back • High water mark (Ratchet): Based on highest anniversary value • Margins for profits controlled by: participation rate/Cap/Spread Equity guarantees hedge • Usually with options (or equivalent) with option budget coming after cost of principal protection • Policyholder behavior (lapse and partial, etc.) still relevant, especially for longer term contracts • Static hedging using OTC options simple but afford less flexibility in product design • Dynamic hedging more flexible and easier to integrate with variable annuities • Dynamic hedging might cause income volatility and expose higher order risks & more model risks 64
  65. 65. Comparison of EIAs and VAs EIAs VAs Short term Long term Sold to fixed income investors who Sold to mutual fund investors who want some want some equity participation downside protection Substantial market risk, little behavior Moderate market risk, more behavior risk and risk, and more like pure derivatives less like pure derivatives (but similar to MBS) Design differentiate sales, often exotic Straight forward designs Equity linked index prices with little Equity linked to total return mutual fund basis risk and net of dividends prices with potentially large basis risk Commonly hedged with OTC structured Commonly hedged dynamically with options exchange-traded futures plus OTC structured options Like a call option Like a put option Guarantees usually in the money Guarantees rarely in the money at maturity 65
  66. 66. Dynamic Policyholder Behavior Modeling GMDB Example GMDB Observations • Drivers: Lapses, surrender charges, partial withdrawals, dollar-for-dollar, proportionate, transfers to the fixed account, transfers to a “safer” separate account fund, interactions with the riders • Certain behaviors can be comparable to moderate changes in economic scenarios for average issue ages • Partial withdrawals on products with dollar-for-dollar GMDB reductions can be significant • Anti-selection from older age issues • Behavioral changes in early policy durations dominate later durations for average issue age • Moderate scenario changes dominate most behavioral changes for older issue ages 66
  67. 67. Dynamic Policyholder Behavior Modeling VAGLB Examples GMIB Observations • Drivers: GMIB utilization, remaining waiting period, ITM/OTM, lapses, transfers to the fixed account, transfers to a safer separate account fund, GMIB guaranteed vs. current annuitization factors • Many behaviors influence capital much more than moderate changes in economic scenarios • Impact of behaviors compounds • Late duration behaviors more important than with GMDB only GMWB Observations • Drivers: GMWB utilization, ITM/OTM, reset, transfers to the fixed account, transfers to a safer separate account fund • Impact of behaviors compounds and is greater than impact of moderate changes in economic scenarios 67
  68. 68. Appendix 2 Advanced computing technology • All contracts are unique and require seriatim modeling and pricing. • Stochastic simulations for complex path dependency & multiple assets • Nested stochastic on stochastic simulations are very time consuming 68
  69. 69. Advanced Computing Technology Challenges Very time consuming using stochastic simulations for almost everything • Path dependency and multiple underlying assets • Complex contract rules and long term contract durations • Integration of GMDB and VAGLB benefits Seriatim computing for daily hedging • All annuity contracts are unique • Can not price correctly two derivatives with averaging • Huge in-force contracts or benefit derivatives to simulate • Policy inforce files are refreshed with new information to recalculate. Nested stochastic on stochastic simulations for hedging projections • Critical for any respectful hedge strategy analysis • Required for some regulatory capital and reserve reporting • Very useful for understanding of long term financial positions • Very comprehensive, complex, and time consuming 69
  70. 70. Advanced Computing Technology Challenges Long Term Financial and Hedging Projections - Systems Large scale distributed processing • Multiple data centers with grid computing farms with hundreds of servers • Automatic failovers and allocation of calculation engines • Scaleable for continued increases in computing demand • Controlled environment Computational finance combined with financial engineering • Close cooperation between financial engineers, actuaries, software developers, system architects for best solutions • Advanced valuation and projection systems • Adaptive to new product designs, derivative instruments, and new strategies. • Use of building block modules • Two separate modules of assets and liabilities but linked together through Greeks and other measures with stochastic optimization 70
  71. 71. Appendix 3 Complex accounting and profitability requirements • Insurance accounting not market consistent • Optimized hedging strategies not clearly defined 71
  72. 72. Accounting vs. Economics Challenges Complex accounting and profitability requirements • Inconsistent rules: market to market vs. conservatism insurance accounting requirements • SOP 03-1 (No Market-to-Market) • FAS 133 (Mark-to-Market) • IFRS (Converging) • New “Principles-based” regulation for VAs and UL products Competing Hedging and Risk Management Objectives • Earnings volatility, economic hedging, tail risks /capital hedging, long term profitability • Optimized hedging strategies not clearly defined • Short term focus for earnings volatility vs. long term focus of economics • Product design and risk management increasingly integrated • Long term projection system critical for optimization • Financial engineering is not in vacuum, at least not just pure economics today Capital and accounting arbitrage? • Economic hedge makes most sense in the long run and in theory • Capital requirements, accounting, and liquidity constraints make things more complex 72
  73. 73. Optimized Hedging Challenges Next generation risk management • Risk exposures managed across product lines instead of by product line • Integrated capital markets and actuarial strategy vs. isolated • Close contact among risk/hedging, pricing, and financial managers • Hedging as a strategic tool to increase sales and improve financial management • Flexible and complementary products with reasonable long term guarantees Enhancements - modify hedge portfolio to account for • Financial management goals • Regulatory / accounting constraints • Views on equity risk premium, interest rate trends • Static portfolio vs. dynamic hedging • Stability, cost, liquidity, adaptability, and applicability • Methodology and criteria for future and ready for implementation • Deep understanding of the markets important: trends and opportunities • Rich / cheap analysis of hedge assets • Deep understanding of the business important: the dynamic profile 73
  74. 74. Appendix 4 Improving the hedging with adaptive learning • Static and dynamic hedging • Path dependency and hedge performance analysis • Key considerations for successful hedging and risk management 74
  75. 75. Static and Dynamic Hedging Options and Futures Dynamically hedge with futures • Introduce risk inherent in volatility assumptions • Extra risks: gap risks, forward volatility risks, transaction costs • Have directional exposure to volatility and there is uncertainty in hedge P/L • Purchase a core block of vanilla options to reduce gamma exposure • Flexible for non-static block of business Hedge with options • The risk reduction and regulatory and financial benefits worth the “cost”? • Supply and demand determines option prices and so implied volatilities. • Wide bid/ask spread for very long dated options • Change in business (new sales and decrements) 75
  76. 76. Static and Dynamic Hedging - Combinations Variable annuity can not be all hedged with a static portfolio of options • Things are not that nice as planned • Things change: new sales, fund transfers, new assumptions, new experience, new market performance, new objectives, etc. Best to replicate with a combination of static options and a dynamic hedging • Very detailed and extensive liability roll forward analysis is needed to account for all changes in the option values of the block of business. • Useful to understand all components of the liability option value changes, to understand trends and behavior, to catch outliers, and to direct potential future improvements. The hedge strategy chosen will affect the residual risks of your product • Analyze trade-offs between tight control of market risk vs. hedge costs • The closer to control market risk, the less flexible for managing policyholder behavior 76
  77. 77. Path Dependency and Adaptive Attribution Analysis Variable annuity liability value is very path dependent • Complicated nature of benefit means that it must be dynamically replicated (but as statically as possible). • VA liability may not be self-evident – only reveled through simulation Extensive option value roll-forward valuation analysis • Very detailed and extensive liability roll forward analysis is needed to account for all changes in the option values of the block of business. • Useful to understand all components of the liability option value changes, to understand trends and behavior, to catch outliers, and to direct potential future improvements. Extensive hedging performance attribution analysis • Hedging is not perfect • Useful to deepen the understanding and gain the insights of the dynamic hedging program performance, to understand the key drivers / assumptions of a dynamic hedging program, to catch the outliers, and to direct potential future improvements. • Important feedback to product design and dynamic policyholder behavior assumptions so that hedging is never too far from where it should be 77
  78. 78. Adaptive Learning: Dynamic Hedging Process 78
  79. 79. Adaptive Learning: Through Hedge Roll-forward Process Annuity Liability option value roll-forward process Ending Beginning Period Period Expected vs. Actual Liability Liability Option Value and Greeks Option Option Value Value Changes in market levels, interest rates, and volatilities New/add-on/backdated premiums Time decay, fees, asset classification Deaths and lapses, withdrawals Transfers of assets between mutual funds Model changes, and other assumption updates, etc. 79
  80. 80. Adaptive Learning: Hedge Performance Attribution Process Net Hedging G/L from: Market risks & Actuarial risks Tracking errors Gamma/Volatility/Interest G/L Policyholder behavior Interests on cash pool & other actuarial elements Trading costs, etc. 80
  81. 81. Key Considerations for Building Stochastic Models Companies generally use stochastic modeling methods to measure the cost of VA guarantees. Stochastic modeling is complex and requires the development of investment return and liability models. A number of issues must be considered when developing these models, including: Economic scenario generator Calibration of investment returns # of scenarios and scenario reduction techniques Product features Projection frequency In-force/new business models Real-world versus risk-neutral scenarios Policyholder behavior Volatility assumptions Risk discount rate Drift assumptions Reinsurance and hedging strategies Correlation assumptions Projection period Mortality assumptions Grouping of funds into indices. 81
  82. 82. Successful Dynamic Hedging and Risk Management For Variable Annuity and EIA Derivatives Guarantees Key Ingredients Computing Computing Technology Technology Expertise Expertise Actuarial Quantitative Actuarial Quantitative Expertise Expertise Expertise Expertise Successful pricing and hedging Exotic Financial and Exotic Financial and Derivatives Capital Derivatives Capital Trading Management Trading Management Expertise Expertise Expertise Expertise 82

×