Pricing Integrated Risk Management Products

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

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. 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. 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. 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. 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. 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

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. 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