1. Pricing Integrated Risk Management Products CAS Seminar on Ratemaking San Diego, March 9, 2000 Session COM-45, Emerging Risks Lawrence A. Berger, Ph.D. Swiss Re New Markets

2. 2 Integrated Products add Capital Market Hedges to Traditional Reinsurance Products Protect against –equity market declines –interest rate increases –foreign exchange losses –corporate bond defaults Client gets more reinsurance protection when investment results are poor

3. 3 Rationale for Integrated Products: Risk is Risk Why protect underwriting results and not investments? Total corporate value depends on both

4. 4 Limit Total Losses from All Sources of Risk XYZ Ins Co ratio of common stocks to premium earned = 50% –Industry ratio of equities to premium = 68% –w/o State Farm = 59% 20% decline in common stocks = 10 loss ratio points

5. 5 Limit Total Losses from All Sources of Risk Integrated aggregate excess of loss program: –Reduce retention by 1 point for every 2% decline in equity portfolio Puts a cap on losses from both sources of risk –Pays if sum of losses from both exceed the original retention –Insurance - (Retention - Financial) = (Insurance + Financial) - Retention

6. 6 Integrated Product Alternatives Integrated features can be added to any type of reinsurance program Aggregate stop loss or per risk excess –Lower attachment point and/or increased limit Multi-year or annually renewable, with additional premiums and profit sharing

7. 7 Pricing Integrated Products Pricing a transaction that combines traditional insurance and capital markets exposures Insurance companies and capital markets take different approaches –But both incorporate expected losses and a risk load Actuarial pricing techniques are used for insurance risks –Calculate expected loss and a separate risk load –Use probability distributions based on historical data and projections of future loss experience

8. 8 Pricing Integrated Products Risk neutral pricing techniques are used for capital market risks –A probability distribution is inferred from market prices arbitrage free because it is consistent with market prices if you sell something that isn’t consistent, you will be arbitraged if you are high, they will sell you short and buy low if you are low, they will buy from you and sell high The probability distribution includes a risk charge –It is based on market prices –No additional risk load is calculated –All-in price

9. 9 Pricing Integrated Products Example: Pricing equity puts (portfolio insurance) –S = S&P 500 value, K = strike price –Payoff is Max(K-S, 0) –Historical distribution is lognormal with mean 11%, standard deviation 20% –Risk neutral distribution is lognormal with mean 5%, standard deviation 25% Expected payoff is higher under the risk neutral distribution

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11. 11 Pricing Integrated Products Expected value under historical distribution is 3.66 (discounted) 99%tile is 30 –Insurance price could be 3.66 + 12.5%*30 = 7.41 Expected value under risk neutral distribution is 7.46 (discounted) In principle, there is no reason why the prices cannot be the same –Will be when risk load for insurers equals risk load for capital markets

12. 12 Pricing Integrated Products How to price integrated products, where insurance risks are combined with capital market risks One approach: –Monte Carlo on the integrated product –Actuarial probabilities for insurance exposures –Risk Neutral probabilities for capital markets exposures –Add a risk charge only for the insurance exposures Use an allocation technique Can be challenging, especially if insurance and capital market exposures are correlated