Market-Consistent
Valuation of
Insurance Contracts
Antoon Pelsser
Professor of Actuarial Science
University of Amsterdam & Netspar
1
Outline
Historical Roots: Actuarial & Finance
 Collapse of Equitable Life
 Market-Consistent Valuation
 New Directions for Actuaries

2
Historical Roots: Actuarial
Life-insurance is “oldest profession”
 1670’s: Valuation of Annuities
 Complex calculations long before
computer-age
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

Deal with uncertainty via conservative
deterministic assumptions

3
Actuarial education more “art” than “science”
Create extra buffers as a “cushion” for risk
Historical Roots: Actuarial (2)
First half of 20th century
 Investment portfolio of life-insurers mainly
bonds
 Investment returns higher than base-rate



Risk-sharing between insurer and policyholder

4
Prudence to cover for “actuarial” risks
“With-profits” insurance policies
Historical Roots: Actuarial (3)
Last quarter of 20th century
 Invest (aggressively) in stocks


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Continue to use traditional actuarial
methods

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5
Higher return than bonds
“Unit-Linked” insurance products
“Prudent” base rate
Profit-sharing
Minimum return guarantees
Historical Roots: Finance
“Meanwhile in banking…”
 1950: Markowitz
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
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1970: Black-Scholes-Merton

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6
Derivative pricing via “Delta-Hedging”
Completely different methodology of
dealing with risk!


Mean-Variance optimisation
Reduce risk via offsetting trading-positions
1980+: Development of risk-management
and supervision in banking
Collapse of Equitable Life

End of 1990’s: Collapse of Equitable Life
in UK



Guaranteed Annuity Option (GAO)



7
Oldest life-insurance company (1762)
Large life-insurance company
Mortality Guarantee (1950’s table)
Interest Rate Guarantee (8%)
Significant change in both risk-factors from
1970 – 1999
Wake-Up Call for Actuaries

Shock for actuaries as “risk professionals”


Severe criticism in UK on the profession
Morris Review of the Actuarial Profession
Market risks are often larger than
insurance risks
 Regulators push for Market-Consistent
Valuation


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8
Denmark, Switzerland, UK, Netherlands
Europe → Solvency II
IASB → Accounting of Insurance Contracts
Market-Consistent Valuation

MC value of Liabilities = Market value of
Replicating Portfolio
Discount cash flows with today’s term structure of
interest rates
 Calculate value of embedded options with arbitragefree pricing
 “Risk-neutral” pricing


9
Different from “classical” Embedded Value
New Directions for Actuaries

Bring “classical” actuaries up-to-speed
with “modern” financial economics



Important steps have already been made
Continuing improvement in the curriculum needed
Change from “risk observer” to “risk
manager”
“Reserve for the risk & wait”…
 Change in attitude is not easy
 Use active risk management (for financial risks)

10
New Directions… (2)

European Insurance Regulators are
developing Solvency II, which is fully
market-consistent based


How to deal with Internal Models?
New proposal from IASB is fully consistent
with market-consistent principles

No consensus (yet) on how to calculate “the”
Market-Consistent value:


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Own Credit Rating
Market Value Margin
New Directions… (3)

“Financial-economic” pricing assumes
“complete market”


Every insurance contract can be replicated by
financial instruments
This is not true for insurance!
Pricing rules in “incomplete” markets
 Mortality risk & trends
 Insurance risks
 (Irrational) Policyholder behaviour
 “With-Profits” contracts

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New Directions… (4)

Find pricing rules that are

Consistent with arbitrage-free pricing for financial
risks
 Extend for non-financial risks
 Utility-based approach seems promising
 Find practical “rules-of-thumb”

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This is currently a field of active academic
research (€1 mln grant from Netspar)