Practical issues in ALM and

Stochastic modelling for

actuaries

Shaun Gibbs FIA

Eric 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 to

Basel II Prudential

Sourcebook

(UK) IFRS

ICA (UK)

EEV

Target Surplus (Aus)

Guarantees

on UL

products

Optimising

Asset

Allocation

Alternative

Investments –

Risk/Return

Real Options Embedded 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 Tails

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Graphically – Fat Tails ASX 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)

• 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 consistent valuations (MCV)

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

Market prices of comparable

market instruments sounds very

fancy!!

• 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

Comparable instrument or

‘replicating asset’ may not exist

• 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?

Key points of MCV

• 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]

Real world – realistic 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

Risk neutral – risk adjusted

cashflows

Real world

+ 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

Comparison of approaches

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!

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?

Which method is best?

• 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

Other issues to think about

• 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?

• 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

Practical application of MCV

• 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

Frictional costs

• 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

MCV AVs – the problem with new

business

Questions????