1. Market-Consistent Valuation of Insurance Contracts
Antoon Pelsser
Professor of Actuarial Science
University of Amsterdam & Netspar 1

2. Outline Historical Roots: Actuarial & Finance
Collapse of Equitable Life
Market-Consistent Valuation
New Directions for Actuaries 2

3. 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 3

4. 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 4

5. 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
Profit-sharing
Minimum return guarantees 5

6. 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 6

7. 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 7

8. 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 8

9. 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 9

10. 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

11. 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 11

12. 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 12

13. 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) 13