Practical issues in ALM and Stochastic modelling for

actuaries

Shaun Gibbs FIAEric McNamara FFA FIAA

• 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

Objectives

Why use Stochastic Models?

Because we want to

Because we have toBasel IIPrudential

Sourcebook (UK) IFRS

ICA (UK)

EEV

Target Surplus (Aus)

Guarantees on UL

products

Optimising Asset

AllocationAlternative

Investments – Risk/Return

Real OptionsEmbedded Options e.g. NNEG

• Mean reversion• Fat-Tails• Arbitrage• Market-Consistent Calibration

Model Features

Mean Reversion Graphically – Exchange Rates

ASD vs USD (1969-present)

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Mean reversion Graphically – Yields

UK 20 Yr Govt Bond Yield (1992-present)

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What is the Consensus?Equity (Capital Values)

Equity (Dividend Yield) Will differ over different industries

Bond Yields At least a band of activity

Inflation Developed countries –Inflation targeting

Exchange Rates Possibly – PPP arguments

Graphically – Fat TailsFTSE 100

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Graphically – Fat TailsASX 200

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• 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

Arbitrage-Free

• 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

Market-Consistent Calibration

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.

Is volatility constant?ASX 200

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Is volatility constant?ASX 200 - % Daily movement

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• 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

Modelling 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

A Topical Problem – Implied Volatility

• Stochastic programming allows us to incorporate contingent events within each simulation

• Some Examples:– 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

• 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

Dynamic Decisions (contd)

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 consistent valuations (MCV)

• MCV of an annuity requires the matching bonds

• MCV of a capital guaranteed bond requires the underlying asset plus a suitable put option

What’s a comparable instrument?

Then we must use financial mathematics to derive or model a synthetic replication to come up with a MCV

Comparable instrument or ‘replicating asset’ may not exist

Deflators are essentially stochastic discount functions

Traditional PV of cashflow = Vt E[ Ct]

MCV PV of cashflow = E[ Vt Ct]

Real world – realistic cashflows

• Adjusted ‘risk neutral’ probabilities

• Risk-free rate

Risk neutral – risk adjusted cashflows

Both approaches will give the same value result

Really depends on the purpose of the valuation

Which method is best?

• 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

Why bother with MCV?

• 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

• How the growth rate will vary with the market

• Traditional approach of a single RDR means that both the EV and new business have a value reduction

MCV AVs – the problem with new business

• Treatment of unsystematic risk means a new business risk adjustment is required to be applied to value new business

• Lower multipliers than a traditional approach?

MCV AVs – the problem with new business

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

• What’s the future role for stochastic techniques in Australia?

• How do we model MC growth rates?

• Would complete development of past correlations with the market adequate for proxy new business MCV?

Some areas for discussion?