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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 Target Surplus (Aus) Prudential Basel II Sourcebook Because we have to EEV (UK) IFRS ICA (UK) Why use Stochastic Models? Optimising Guarantees Asset on UL Allocation products Because we want to Alternative Real Options Investments – Embedded Options e.g. NNEG Risk/Return Model Features • Mean reversion • Fat-Tails • Arbitrage • Market-Consistent Calibration 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 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 7/ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Mean reversion Graphically – Yields UK 20 Yr Govt Bond Yield (1992-present) 12 10 8 6 4 2 0 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 What is the Consensus? Equity (Capital Values) (cid:56) Equity (Dividend Yield) (cid:57) Will differ over different industries Bond Yields (cid:57) At least a band of activity Inflation (cid:57) Developed countries – Inflation targeting Exchange Rates Possibly – PPP arguments Graphically – Fat Tails FTSE 100 0.180000 0.160000 0.140000 0.120000 0.100000 FTSE 100 Normal 0.080000 0.060000 0.040000 0.020000 0.000000 -0.0542-20.5095-101.20348-002.00144-901.70241-801.40338-701.10435-600.80432-500.50529-400.02626-209.90723-109.608200-90.30916-909.101-308.80810-708.50107-608.20204-507.9030104.700614602.605054702.904067803.203108903.502194003.801271104.101230204.400243304.609266404.908279505.207392605.507351705.806328806.105414906.404455006.703478170.00259102.70352437612 Graphically – Fat Tails ASX 200 0.14 0.12 0.1 0.08 ASX 200 Normal 0.06 0.04 0.02 0 2 6 8 6 3 1 9 7 5 2 9 1 3 5 8 1 2 5 7 1 3 0 5 0 5 9 4 9 4 0 2 4 6 8 7 3 5 7 6 5 1 8 6 3 0 8 5 3 6 6 1 6 1 1 2 7 2 8 0 2 8 5 2 9 5 2 9 0 1 4 6 9 0 4 6 9 3 3 7 3 0 7 3 0 7 3 0 7 0 3 6 6 3 6 9 3 0 2 2 2 1 1 1 0 0 0 2 6 9 2 1 9 2 5 -0.0 -0. -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0. 0.00 0.00 0.00 0.01 0.0 0.01 0.02 0.02 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

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Demystify some terms. • Issues around model selection. • Awareness of key choices. • Practical problems in model/parameter selection. • Demystify market-

Practical issues in ALM and Stochastic modelling for actuaries PDF

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Demystify some terms. • Issues around model selection. • Awareness of key choices. • Practical problems in model/parameter selection. • Demystify market-

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