Practical issues in ALM and Stochastic modelling for actuaries

31 Pages·2007·0.2 MB·English

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