2006 Quant Congress USA

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Costly GMWB in Bear Markets
14

15. Costly GMWB Reset in Bull Market
15

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

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. 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. 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. 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

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. 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

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. 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

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. 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. 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. 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. 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. 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

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36. 36

37. 37

38. 38

39. 39

40. 40

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Your Questions & Comments
The future of integrated financial engineering and actuarial science is here

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. 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. Variable Annuity Contracts
Living Benefits Comparisons
58

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. 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. 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. Costly GMIB in Bull Market
62

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. 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. 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. 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. 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. 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. 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. 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. Appendix 3
Complex accounting and profitability requirements
• Insurance accounting not market consistent
• Optimized hedging strategies not clearly defined
71

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. 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. 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. 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. 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. 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. Adaptive Learning:
Dynamic Hedging Process
78

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. 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. 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. 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