Session 76 PD, Modeling Indexed Products Moderator: Leonid Shteyman, FSA Presenters: Trevor D. Huseman, FSA, MAAA Leonid Shteyman, FSA
Modeling Indexed Products Trevor Huseman, FSA, MAAA Managing Director Miller & Newberg, Inc. Trevor.Huseman@miller-newberg.com
Agenda General Modeling Considerations Indexed Product Basics Modeling Challenges Performance Improvements
General Modeling Considerations Cost Time and effort required to develop and maintain model Will additional staff, consulting resources, or new software be needed? Accuracy Has the model been sufficiently validated? How well does model reflect company practice and reality? Efficiency Are runtimes reasonable given the functionality? Streamline process for updating and getting results out of model Versatility Can the model be used for multiple purposes? What are the limitations? Transparency Do the users as well as management understand the input/output of the model? Are the methodologies used explainable?
What is an Indexed Product? Total fund value made up of multiple accounts Account(s) with performance linked to an index Account value(s) cannot decrease due to index performance Index credits generally applied only at end of crediting term Generally includes a fixed account option
Crediting Indices Equities S&P 500 NASDAQ 100 Dow Jones Industrial Average Russell 2000 FTSE 100 Combination (blended) Other Bond index Interest rate Gold Real estate Volatility control index Other
Crediting Mechanics Methodologies Point-to-point Monthly average Monthly point-to-point Performance trigger Other Parameters Cap Participation rate Fee (spread) Controlled index
Annual PTP Crediting Example Up Scenario Cap = 6% Index BOY = 1,000 Index EOY = 1,100 Index Growth = 10% Index Credit = Min(10%, 6%) = 6% Fund Value BOY = 10,000 Fund Value EOY = 10,600 Down Scenario Cap = 6% Index BOY = 1,000 Index EOY = 900 Index Growth = -10% Index Credit = Max(-10%, 0%) = 0% Fund Value BOY = 10,000 Fund Value EOY = 10,000
Annual PTP Static Hedge Example Index BOY = 1,000 Cap = 6% Hedge components: Purchase at-the-money call option, strike = 1,000 Sell out-of-the-money call option, strike = 1,060 Time to maturity of options is one year Hedge payoff should closely reflect index credits
Cap Setting Example Asset yield = 4.5% Pricing spread = 2.0% Option budget = 2.5% Determine cap with option cost equal to option budget Cap = 6.9% Cap (%) 14 12 10 8 6 4 2 Sample Option Cost by Cap 0 1 2 3 4 Option Cost (%)
Modeling Challenges Complexity and number of calculations Requires index assumptions and expertise Hedging issues High development time and costs Excessive runtimes and/or memory usage
Numerous and Complex Calculations Multiple funds/buckets/parameters to track Liability-only runs not suitable hedge must be tracked Solvers for cap, participation rate, fee Generally an iterative process Must define which parameter to solve for Market value calculation of options Required for hedges and AG35 reserving Some options don t have closed form solution May require Monte Carlo simulation or some type of approximation Increases model development effort and runtime Makes model review and maintenance difficult
Index and Option Assumptions Index growth Inconsistent year to year Not appropriate to do deterministic runs assuming historical average growth rate Stochastic modeling generally appropriate May be reasonable to test deterministic growth rate equal to option budget Implied volatility Data may be hard to gather Generally varies by ratio of strike to index as well as time to maturity, creating a volatility surface Dividend yield Risk-free rate
Volatility Impact on Option Price Impact of volatility will vary Increasing volatility may increase or decrease price depending on option type Diminishing impact as expiry nears Impacted by ratio of strike to index Option Cost (%) 12 10 8 6 4 2 0 Black-Scholes Example 1-Year At-the-Money Option 10 15 20 25 30 Volatility (%)
Volatility Impact on Account Performance Hypothetical account performance of annual point-to-point strategy Based on S&P 500 index starting on Jan 4, 2003 Hypothetical caps using Black-Scholes formula: 12% vol 8.5% cap 15% vol 7.5% cap 25% vol 6.7% cap Account Value (000s) 220 200 180 160 140 120 100 Account Value by Year 0 1 2 3 4 5 6 7 8 9 10 11 12 Year 6.7% Cap 7.5% Cap 8.5% Cap
Hedging Issues Hedge ratio Common to hedge only for policyholders expected to persist to end of crediting term Must determine appropriate decrement assumptions in model Hedge costs Company may have dynamic hedging process, but model has limited dynamic capabilities Company may incur dealer premiums on options As a result, actual hedge costs differ from model hedge costs Hedge mismatch Common to group policies across issue dates to attain adequate hedging volume, so hedges don t perfectly reflect the liability Does model hedging occur at policy or aggregate level? Models often assume perfect hedge
Performance Improvements Enhance hardware / grid computing capabilities Pros: don t have to sacrifice accuracy of model Cons: high cost, may require additional staff/expertise, benefit may be limited by actuarial software Model compression (inforce) Pros: don t have to sacrifice model functionality Cons: time/expertise required to perform compression, loss of accuracy Crediting strategy mapping Pros: simple to perform once mappings established Cons: must determine appropriate mappings, loss of accuracy Reduce number of premium buckets Pros: likely simple to implement Cons: loss of accuracy, may not be suitable for products with high renewal volume
Crediting Strategy Mapping Goal is to improve model performance by reducing number of accounts being modeled Map complex or low volume strategies to other crediting accounts Considerations for mapping: Are the option budgets consistent? How similar are the crediting methodologies? How correlated are the indices? Are the crediting parameters the same? Combine accounts that are expected to perform similarly
2015 SOA Life and Annuity Symposium Market Consistent Pricing of Fixed Indexed Annuities May 5, 2015 Lenny Shteyman VP & Actuary, Corporate Pricing Oversight
Agenda Background: Market Consistent Pricing Fixed vs Variable Annuities FIA dynamic lapse example Issues: Rising interest rates dynamics Modeling implied volatility Modeling investment strategy 2
Market Consistent Pricing Popular framework in EU Pros: eliminates the art of developing the discount rate eliminates reliance on investment performance vs other margins enhances consistency with other business units and companies Cons: still leaves room for interpretation modeling complexity Market consistent vs risk free vs arbitrage free 3
Market Consistent Scenario Creation Generate 1,000 stochastic scenarios Calibrate to current observable prices of investments bonds, equities, equity options, swaptions, etc. Martingale Tests validate calibrated scenario set for absence of risk premium typically only at time 0 Let s hope that this pricing tool reasonably prices less liquid, exotic, market-dependent insurance contracts! Liquidity Premium 4
Fixed vs Variable Annuities Investment risk entirely transferred to client in VA Fixed Annuities require investment in long duration assets for competitive crediting strategies Fixed Annuities have surrender charges and MVA to protect against disintermediation, alas, not entirely. Minimum Non-Forfeiture Guarantee for Fixed Annuities 87.5% of Initial Premium growing at 1% per year 5
Fixed Annuity MVA Example Sample FIA Product: 10% 1 st year expense, including commission 10% declining surrender charge 10 years average portfolio maturity Economics: low expected lapse in year 1, however, if surrendered, MVA can recover only 2.5% of Premium in excess of the 1 st year expense 2.5% is quite limited protection against rising interest rates if the portfolio is invested long if the AV increases 10%, MVA can recover as much as 12.5% 6
Dynamic Lapse Example Dynamic Lapse Rate portfolio yields and crediting strategy are fairly inflexible after issue if rates increase after issue, the original crediting strategy is no longer attractive hypothetical example: Rate Increase <1% 1% 2% 3% 4% >5% Additional Lapse 0% 0.5% 3% 7% 15% 25% 7
Now, let s talk about issues! 8
Rising Interest Rates MC projected rates follow the implied forward curve Bond losses: more frequent than gains because average scenario rate is rising after issue more severe than gains due to dynamic lapse MVA: less effective due to low average equity returns FIAs don t look favorable under (rising rates) MCEV view Contrast with VA 9
Modeling implied volatility stochastically Term structure of equity options normally suggests future implied volatility increases. Hypothetical example: option maturity 1 2 3 4 5 6 implied volatility, spot 15% 16% 18% 19% 21% 23% implied 1 year volatility, forward 15% 17% 21% 22% 28% 31% Approaches to stochastic volatility modeling: Approach 1 Approach 2 Approach 3 Approach 4 Modeling indexed product yes yes yes no Modeling volatility yes yes yes no Scenario dependent yes no no no Term Structure Consistent yes yes no no Historical Mean Reverting no no yes no Market Consistent yes kind of no yes! Calibration challenging regular regular simple Approach 4 ignores volatility altogether, models non-indexed fixed annuity, and implicitly assumes hedges can support crediting strategy 10
Investment Strategy All MC assets earn the same risk-free return, on average actual crediting strategy in year 1 relies on earning credit spread modeled strategy in year 1 will be either subsidized or unrealistic Scenarios are typically calibrated for buy-and-hold, at time 0 only. However, this calibration may be insufficient many bonds are sold before maturity due to dynamic lapses assets backing AV increases are reinvested at future new money rates 11
In Conclusion Modeling challenges with MCEV view for FIAs volatility and investment strategy Challenges in generating attractive MCEV results liquidity premium < actual credit spread upward sloping yield curve Explore MCEV-friendly product features e.g. explicit fees that can pierce the 0% minimum crediting rate Combo with GMXB rider Underlying AV that can t go down due to equities makes the cost of the rider insignificant Current rider price for FIA+GMXB combo is similar to VAs 12
Questions and Answers??? 13