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Market-Consistent Valuation of Insurance Contracts. Antoon Pelsser Professor of Actuarial Science University of Amsterdam & Netspar. Historical Roots: Actuarial & Finance Collapse of Equitable Life Market-Consistent Valuation New Directions for Actuaries. Outline.

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market consistent valuation of insurance contracts

Market-Consistent Valuation of Insurance Contracts

Antoon Pelsser

Professor of Actuarial Science

University of Amsterdam & Netspar


Historical Roots: Actuarial & Finance

Collapse of Equitable Life

Market-Consistent Valuation

New Directions for Actuaries



historical roots actuarial
Life-insurance is “oldest profession”

1670’s: Valuation of Annuities

Complex calculations long before computer-age

Actuarial education more “art” than “science”

Deal with uncertainty via conservative deterministic assumptions

Create extra buffers as a “cushion” for risk

Historical Roots: Actuarial


historical roots actuarial 2
First half of 20th century

Investment portfolio of life-insurers mainly bonds

Investment returns higher than base-rate

Prudence to cover for “actuarial” risks

Risk-sharing between insurer and policy-holder

“With-profits” insurance policies

Historical Roots: Actuarial (2)


historical roots actuarial 3
Last quarter of 20th century

Invest (aggressively) in stocks

Higher return than bonds

“Unit-Linked” insurance products

Continue to use traditional actuarial methods

“Prudent” base rate


Minimum return guarantees

Historical Roots: Actuarial (3)


historical roots finance
“Meanwhile in banking…”

1950: Markowitz

Mean-Variance optimisation

1970: Black-Scholes-Merton

Derivative pricing via “Delta-Hedging”

Completely different methodology of dealing with risk!

Reduce risk via offsetting trading-positions

1980+: Development of risk-management and supervision in banking

Historical Roots: Finance


collapse of equitable life
End of 1990’s: Collapse of Equitable Life in UK

Oldest life-insurance company (1762)

Large life-insurance company

Guaranteed Annuity Option (GAO)

Mortality Guarantee (1950’s table)

Interest Rate Guarantee (8%)

Significant change in both risk-factors from 1970 – 1999

Collapse of Equitable Life


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

Denmark, Switzerland, UK, Netherlands

Europe → Solvency II

IASB → Accounting of Insurance Contracts

Wake-Up Call for Actuaries


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 arbitrage-free pricing

“Risk-neutral” pricing

Different from “classical” Embedded Value

Market-Consistent Valuation


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)

New Directions for Actuaries


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:

Own Credit Rating

Market Value Margin

New Directions… (2)


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

New Directions… (3)


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”

This is currently a field of active academic research (€1 mln grant from Netspar)

New Directions… (4)