Introduction to Derivative Products and DFA

1. Introduction toDerivative Productsand DFA • Lawrence A. Berger, Ph.D. • Swiss Re New Markets • Daniel B. Isaac, FCAS • Falcon Asset Management Division of Swiss Re • DFA Seminar: Managing Risk in a Portfolio Context

2. What Is A Derivative? • Financial instrument whose value is derived from the performance of an “underlying asset” • Refer to “cash price,” or “spot price” of the underlying

3. What Is An Underlying Asset? • Can be anything • Performance should be quantifiable • Some examples are: • Interest Rates • Equities • Foreign Exchange Rates • Commodities • Indices • Loss Ratios

4. How Is A Derivative Created? • Derivative product is a contractual agreement between two parties to either: • exchange cash flows, or • have one party assume a risk of the other party for a price • Derivative product uses the “underlying asset” as a basis for the exchange

5. Options • An Option Contract gives the owner the right, but not the obligation, to buy or sell an underlying asset at an exercise price on or before an agreed date • Call = Right to buy at X • Put = Right to sell at X

6. Options V V Buy A Call Buy A Put P P V V Sell A Put Sell A Call P P

7. Intrinsic value Options • Options have a Time Value and an Intrinsic Value V Call option value Time value P

8. Options Summary • Intrinsic Value • Call = Max(P-X,0) • Put = Max(X-P,0) • Option Premium = Intrinsic value plus time value

9. Pricing an Option • Calculations dependent on several factors • Spot price of underlying asset • Strike price - price at which option allows owner to purchase or sell underlying asset • Interest rates • Volatility - measure of frequency and relative size of changes in price of underlying asset • Time to expiration

10. Volatility Low Vol. Asset Probability High Vol. Asset Price of Underlying Asset Fwd Price Strike Price

11. Interest Rate Cap • An agreement where the seller agrees to pay the buyer, in return for a premium, the difference between the reference rate and an agreed strike rate should the reference rate rise above the strike

12. Cap Payoff Profile Gain/Loss Cap Interest Rate Premium Strike

13. Cap = Hedge High Rates • An interest rate cap is essentially an insurance policy against interest rates rising • A cap buyer is protected against rates rising beyond the strike • A cap seller receives a fee and gives up return if rates rise beyond strike

14. Double Trigger Cover Interest Rates Decrease Increase No Cover Sell Assets, Pay Losses Covered Collect Reinsurance • Reinsured pays a premium to purchase cover if two different risk events occur • The correlations between the two events are low or non-existent • Lack of correlation allows for lower premiums • Example: interest rate option with catastrophe trigger • Option protects against losses on portfolio of fixed income instruments • Option is exercisable only after Cat event Yes Catastrophic Event No No Cover, No Losses No Cover, No Losses

15. Double Trigger CoverEquity Protection Stock Market Increase Decline No Cover Sell Assets, Pay Losses Covered Collect Reinsurance Yes Catastrophic Event No No Cover, No Losses No Cover, No Losses

17. PCIC Company Profile • Primarily short-tailed property business • Large portion (~50%) of book is CAT exposed • As a result of large liability risk, very conservative investment strategy: 20% cash, 80% bonds

18. Traditional Cover • Aggregate CAT cover: 300 x 100 calendar year loss ratio from CATs • Price: 30% of subject earned premium • Placement: 50% • No reinstatements or rebates

19. Dual Trigger Cover Income Smoothing • Aggregate CAT cover: 300 x 100 calendar year loss ratio from CATs • Recovery reduced based on S&P 500 return: • Below 0%: No reduction • Above 20%: Zero recovery • Between 0% and 20%: Pro-rata reduction • Price: 12.5% of subject earned premium • Placement: 100% • No reinstatements or rebates

20. Shareholder's Equity Efficient Frontier 3-Year Time Horizon 880.0 860.0 840.0 820.0 800.0 780.0 Shareholder's Equity ($mm) Current Reinsurance 760.0 740.0 720.0 700.0 140.0 160.0 180.0 200.0 220.0 240.0 260.0 280.0 Standard Deviation of Shareholder's Equity ($mm) Current

21. Shareholder's Equity Efficient Frontier 3-Year Time Horizon 880.0 860.0 840.0 820.0 800.0 780.0 Current Reinsurance 760.0 740.0 Traditional Cover 720.0 700.0 110.0 130.0 150.0 170.0 190.0 210.0 230.0 250.0 Shareholder's Equity ($mm) 270.0 290.0 Standard Deviation of Shareholder's Equity ($mm) Current Traditional Cover Efficient Frontier

22. Shareholder's Equity Efficient Frontier 3-Year Time Horizon 880.0 860.0 840.0 820.0 800.0 780.0 Shareholder's Equity ($mm) Current Reinsurance 760.0 Dual Cover 740.0 Traditional Cover 720.0 700.0 110.0 130.0 150.0 170.0 190.0 210.0 230.0 250.0 270.0 290.0 Standard Deviation of Shareholder's Equity ($mm) Traditional Cover Current Dual Cover Efficient Frontier

23. Myth Company Profile • Similar book to PCIC • More heavily reinsured • More aggressive investment strategy: 50% stocks, 50% short-term bonds

24. Traditional Cover • Aggregate CAT cover: 300 x 100 calendar year loss ratio from CATs • Price: 25% of subject earned premium • Placement: 50% • No reinstatements or rebates

25. Dual Trigger Cover Catastrophe Protection • Notional Amount: 75% of earned premium • Trigger: Calendar year loss ratio of at least 75% • Recovery based on S&P 500 return: • Below -20%: 100% of notional • Above 0%: Zero recovery • Between 0% and -20%: Pro-rata reduction • Price: 3% of earned premium • Placement: 100% • No reinstatements or rebates