Practical issues in ALM and Stochastic modelling for actuaries Shaun Gibbs FIA Eric McNamara FFA FIAA
Objectives Demystify some terms Issues around model selection Awareness of key choices Practical problems in model/parameter selection Demystify market-consistency Practical problems with market-consistent valuations
Prudential Sourcebook (UK) Target Surplus (Aus) Because we have to Basel II IFRS EEV ICA (UK) Why use Stochastic Models? Optimising Asset Allocation Because we want to Real Options Embedded Options e.g. NNEG Guarantees on UL products Alternative Investments Risk/Return
Model Features Mean reversion Fat-Tails Arbitrage Market-Consistent Calibration
31/07/69 31/07/70 31/07/71 31/07/72 31/07/73 31/07/74 31/07/75 31/07/76 31/07/77 31/07/78 31/07/79 31/07/80 31/07/81 31/07/82 31/07/83 31/07/84 31/07/85 31/07/86 31/07/87 31/07/88 31/07/89 31/07/90 31/07/91 31/07/92 31/07/93 31/07/94 31/07/95 31/07/96 31/07/97 31/07/98 31/07/99 31/07/00 31/07/01 31/07/02 31/07/03 31/07/04 31/07/05 31/07/06 Mean Reversion Graphically Exchange Rates ASD vs USD (1969-present) 1.6000 1.4000 1.2000 1.0000 0.8000 0.6000 0.4000 0.2000 0.0000
11/02/92 11/08/92 11/02/93 11/08/93 11/02/94 11/08/94 11/02/95 11/08/95 11/02/96 11/08/96 11/02/97 11/08/97 11/02/98 11/08/98 11/02/99 11/08/99 11/02/00 11/08/00 11/02/01 11/08/01 11/02/02 11/08/02 11/02/03 11/08/03 11/02/04 11/08/04 11/02/05 11/08/05 11/02/06 11/08/06 11/02/07 11/08/07 Mean reversion Graphically Yields UK 20 Yr Govt Bond Yield (1992-present) 12 10 8 6 4 2 0
What is the Consensus? Equity (Capital Values) Equity (Dividend Yield) Will differ over different Bond Yields industries At least a band of activity Inflation Developed countries Inflation targeting Exchange Rates Possibly PPP arguments
Graphically Fat Tails FTSE 100 0.000000 0.020000 0.040000 0.060000 0.080000 0.100000 0.120000 0.140000 0.160000 0.180000-0.0542259-0.051123-0.0480201-0.0449172-0.0418143-0.0387114-0.0356084-0.0325055-0.0294026-0.0262997-0.0231968-0.0200939-0.016991-0.013888-0.0107851-0.0076822-0.0045793-0.0014764 0.00162655 0.00472946 0.00783238 0.01093529 0.01403821 0.01714113 0.02024404 0.02334696 0.02644987 0.02955279 0.03265571 0.03575862 0.03886154 0.04196445 0.04506737 0.04817029 0.0512732 0.05437612 FTSE 100 Normal
Graphically Fat Tails ASX 200 0.14 0.12 0.1 0.08 0.06 ASX 200 Normal 0.04 0.02 0-0.0338612-0.030536-0.0272108-0.0238856-0.0205603-0.0172351-0.0139099-0.0105847-0.0072595-0.0039342-0.000609 0.00271621 0.00604143 0.00936665 0.01269188 0.0160171 0.01934232 0.02266755 0.02599277
Arbitrage-Free A model that produces outputs permitting arbitrage opportunities implies that the user can predict certain future profits Modern models produce arbitrage-free outcomes e.g. yield curves
Market-Consistent Calibration Much demand for models that can produce market-consistent valuations That is, the ability to calibrate the model to current market prices Some models (e.g. The Smith Model, Barrie & Hibbert) are designed to incorporate MC calibrations Older ones e.g. Wilkie are not Importance depends on purpose of modelling
Impact of Model Choice Source: Creedon S (and 10 other authors), 2003 Risk and Capital Assessment and Supervision in Financial Firms, Interim Working Party Paper, Finance and Investment Conference 2003.
Impact of Model Choice Source: Creedon S (and 10 other authors), 2003 Risk and Capital Assessment and Supervision in Financial Firms, Interim Working Party Paper, Finance and Investment Conference 2003.
17/10/01 17/12/01 17/02/02 17/04/02 17/06/02 17/08/02 17/10/02 17/12/02 17/02/03 17/04/03 17/06/03 17/08/03 17/10/03 17/12/03 17/02/04 17/04/04 17/06/04 17/08/04 17/10/04 17/12/04 17/02/05 17/04/05 17/06/05 17/08/05 17/10/05 17/12/05 17/02/06 17/04/06 17/06/06 17/08/06 17/10/06 17/12/06 17/02/07 17/04/07 17/06/07 Is volatility constant? ASX 200 7000 6000 5000 4000 3000 2000 1000 0
18/10/01 18/12/01 18/02/02 18/04/02 18/06/02 18/08/02 18/10/02 18/12/02 18/02/03 18/04/03 18/06/03 18/08/03 18/10/03 18/12/03 18/02/04 18/04/04 18/06/04 18/08/04 18/10/04 18/12/04 18/02/05 18/04/05 18/06/05 18/08/05 18/10/05 18/12/05 18/02/06 18/04/06 18/06/06 18/08/06 18/10/06 18/12/06 18/02/07 18/04/07 18/06/07 Is volatility constant? ASX 200 - % Daily movement 4.00% 3.00% 2.00% 1.00% 0.00% -1.00% -2.00% -3.00% -4.00%
Modelling Volatility Many approaches to deal with non-constant volatility: ARCH family: Error term is heteroscedastic and auto-correlated, allowing runs of high and low volatility Ornstein-Uhlenbeck: Model volatility as a mean reverting stochastic process Markov regime switching: Model economy as having states with varying volatility characteristics. Transition matrices govern movements between states
A Topical Problem Implied Volatility Reverse Mortgages incorporate the No Negative- Equity Guarantee an embedded put option for the borrower Our risky assets here are: The value of the Property Short term interest rates (if loan is variable rate) Valuing this put option require a property model How volatile is an individual house price? How does volatility differ between geographical areas? Some data available on mean house prices, but moving prices for an individual property not available One solution is to merge knowledge of volatility in mean price index and distribution of price around mean
Stochastic programming allows us to incorporate contingent events within each simulation Some Examples: Dynamic Decisions Policyholder decisions: Lapses/renewals/new business/policy conversions related to economic conditions Management decisions: Asset allocation, premium rates, closure to NB Modelling policyholder decisions means fully allowing for contingent risks Modelling management decisions means allowing for reasonably foreseeable action, usually to prevent insolvency or improve performance
Dynamic Decisions (contd) Some considerations: Contingent actions of policyholders need to have credible backing evidence Management decisions need to be based on business plans, contingency arrangements and best-practice Need to allow for any delays in action i.e. cure unlikely to be applied instantaneously
Market consistent valuations (MCV) The concept of market consistent valuation is here to stay. Areas of application include International Financial Reporting Standards (IFRS), European Embedded Value (EEV) and Solvency II In essence, the concept is to place a value on liabilities in a manner which is consistent with how the market prices comparable financial instruments
Market prices of comparable market instruments sounds very fancy!! Not when you break it down to basics MCV of an annuity requires the matching bonds MCV of a capital guaranteed bond requires the underlying asset plus a suitable put option
Comparable instrument or replicating asset may not exist This is a common scenario Then we must use financial mathematics to derive or model a synthetic replication to come up with a MCV 2 main methods exist. They are: Real world methods with deflators Risk neutral methods
Key points of MCV Is there a replicating asset? Are we calibrated to the market? Are we arbitrage free (there should be a unique price for an asset)? Do we use risk neutral or real world?
Real world realistic cashflows Real world techniques involve projecting realistic cashflows and using deflators to discount them Deflators are essentially stochastic discount functions Traditional PV of cashflow = Vt E[ Ct] MCV PV of cashflow = E[ Vt Ct]
Risk neutral risk adjusted cashflows The probabilities in the expected cashflows in real world are realistic but in risk neutral they are adjusted risk neutral probabilities Rather than apply a deflator to value a cashflow, the risk neutral approach uses the risk-free rate The MCV should be the same whether we use real or risk neutral
Real world Comparison of approaches + Cashflows can be used for planning/forecasting + Real world method is more transparent + Potentially quicker as only one model required for valuation and planning results - Mathematically more complicated as deflators are required - More difficult to calibrate to the market due to the complexity involved - Harder to understand and explain
Risk Neutral + A mathematically simpler approach to achieving a market consistent valuation + Easier to calibrate to market + Results are easier to explain as based on risk free rates and not deflators + More understood as banks have been using this method for some time - Cashflows are not the realistic expected cashflows and so cannot be used for planning/forecasting - Must run two models, one for valuation and one for cashflow projections
It depends! Which method is best? Both approaches will give the same value result. Really depends on the purpose of the valuation i.e. is it say checking solvency at a point in time? Or is it a planning exercise that requires realistic cashflows?
Other issues to think about Objectivity? Still have to choose a statistical distribution. Still have to think about tails, reversion etc. Subjective? Incomplete/inefficient markets as highlighted in Deflators Demystified by Joshua Corrigan et al (2007). In such cases we cannot reliably model in a MC fashion
Why bother with MCV? Being objective as calibrated by the market? Prevent any issues such as artificial value creation through changing the asset mix. Produce a fair value of liabilities Place an appropriate value on options and guarantees
Practical application of MCV The MCV approach is becoming popular in AV/EV/EEV work. In particular, EEV methodology was born to enhance the consistency between EV results in Europe. The MCV approach is a natural choice for this as: Removes subjectivity in results caused by selection of a risk discount rate More appropriate modelling of the cost of guarantees and options Does not allow the creation of value by changing the asset mix
Frictional costs MCV methodologies only address systematic risk. MCV assumes that all unsystematic risks are diversifiable as in pure financial theory However, development in this area has shown there is a cost/reward for these unsystematic risks in the form of frictional costs. These frictional costs are often used as the balancing item to explain the differences between MCV and traditional methods
Frictional costs Main sources are as follows: Agency costs - management decisions Cost of financial distress - financial difficulties Transaction costs - salaries etc Neutrality of taxes - asymmetric taxes
MCV AVs the problem with new business We have shown that you can calibrate to the market for investment returns but how do you calibrate to market growth rates for life insurance business? This is more of an issue in situations where the value of future new business is significant. And this is often the case in the Australian market
MCV AVs the problem with new business There is no obvious method to calculate a market consistent growth rate. Therefore, when applying a new business multiplier we need to think of how the growth rate will vary with the market Wealth management products positively correlated with market risk products less so..others?
MCV AVs the problem with new business In a traditional appraisal value, a single discount rate is often applied to both the inforce and new business. This discount rate includes implicit allowances for business risks including the risks associated with selling new business Effectively, this means that both the EV and new business have a value reduction
MCV AVs the problem with new business In a MCV AV, by definition, there is only allowance for market risk. Therefore, an adjustment is required to be made to the new business component to allow for the unsystematic new business risk Unlike a traditional method, this value reduction will be captured completely in the new business value
MCV AVs the problem with new business Therefore, all else being equal, the market consistent multiplier will potentially be lower than the corresponding traditional multiplier. However, to what degree is difficult to quantify The real solution lies in the ability to develop a stochastic growth rate with a distribution that is based on market data. This most likely means a different new business multiplier for each product type
MCV AVs the problem with new business HOW??? Calibrate to what? No suitable assets exist Proxy MCV to calibrate to recent market transactions. A workaround and not MC in the true sense We require a method to derive an appropriate level of correlation between growth rates and the market returns
Questions????