1. Derivatives Workshop Actuarial Society October 30, 2007

2. Agenda • Intro to Derivatives • Buying/Short-selling • Forwards • Options • Swaps

3. What are Derivatives? • A financial instrument that has a value determined by price of something else • A contract whose value depends on what something else is worth • Futures –Options • Swaps – Insurance

4. Why use Derivatives? • Risk management • Hedging • Speculation • Reduced transaction costs • Regulatory arbitrage

5. Buying an Asset - Long Position • Offer price (ask price) • Bid price • Bid-ask spread • Commission (flat or percentage)

6. Example • Bid price = $50; Ask price = $50.25 • Commission = $1/transaction • How much does it cost to buy 100 shares, then immediately sell it? • Cost = $50.25*100 - $50*100 + $2 = $27

7. Short-Selling • Borrow now • Sell now • Buy later (covering the short position) • Return later • Lease rate of asset – payments that must be made before repaying asset

8. Why Short-sell? • Speculation • Financing • Hedging

9. Example • Stock price now = $50 • Stock price one year from now = $49.50 • Commission = $1/transaction • How much can you make short selling 100 shares? • Profit = $50*100-$49.50*100-$2 = $48

10. Forward Contracts • Sets terms now for the buying or selling of an asset at specified time in future • Specifies quantity and type of asset • Sets price to be paid (forward price) • Obligates seller to sell and buyer to buy • Settles on expiration date

11. Forward Contracts • Forward price -- price to be paid • Spot price -- market price now • Underlying asset -- asset on which contract is based • Buyer = long; Seller = short • Long position makes money when price • Short position makes money when price

12. Payoffs in Forward Contract • Payoff to long forward (buyer) = Spot price at expiration - forward price • Agreed to buy at fixed (forward) price • Payoff to short forward (seller) =Forward price - spot price at expiration • Agreed to sell at fixed price

13. Call Options • Contract where buyer has the right but no obligation to buy • Seller is obligated to sell, if the buyer chooses to exercise the option • Since seller cannot make money, buyer must pay premium for option • Forwards have no premium

14. Call Options • Strike price - amount buyer pays for the asset • Exercise - act of paying strike price to receive the asset • Expiration - when option must be exercised, or become worthless • European style - only exercise on x-date • Bermudan style - during specified periods • American style - entire life of option

15. Payoff of Call Option - Long • Buyer is not obligated to exercise -- will only do so if payoff is greater than 0 • Purchased call payoff =max[0, spot price at x-date - strike price] • Must pay premium to seller • Profit = payoff - future value of premium

16. Payoff of Call Option - Short • Opposite to payoff/profit of buyer • Written call payoff =-max[0, spot price at x-date - strike price] • Only profits from premium • Profit = - payoff + future value of premium

17. Put Options • Contract where seller has the right but no obligation to sell • Buyer is obligated to buy, if the seller chooses to exercise the option • Since buyer cannot make money, seller must pay premium for option • Seller of asset = buyer of put option

18. Insurance Strategies • Buying put option – floor (min sale price) • Buying call option – cap (max price) • Covered writing – writing option with corresponding long position • Naked writing – no position in asset

19. Covered writing • Covered call • Same as selling a put • Asset whose price is unlikely to change • Covered put • Same as writing a call

20. BUY CALL & SELL PUT Must pay net option premium Pay strike price FORWARD CONTRACT Zero premium Pay forward price Synthetic Forwards

21. Put-Call Parity • No arbitrage • Net cost of index must be same whether through options or forward contract Call (K,T) – Put(K,T) = PV(F0,T – K)

22. Spreads – Only calls/only puts • Bull: buy call, sell call with higher strike price • Bear: buy higher strike price, sell lower • Box: synthetic long forward and synthetic short forward at different prices • Ratio spread: buy m calls and sell n calls at different strike prices • Can have zero premium (only pay if you need the insurance)

23. Collars • Buy put, sell call with higher strike • Collar width – difference between call and put strikes • Similar to short forward contract

24. Straddles • Buying call and put with same strike price • Profits from volatility in both directions • Premiums are costly (paying twice)

25. Strangle • Same as straddle, but buy out-of-the-money options • Premiums will be lower • Stock price needs to be more volatile in order to make profit

26. Written Straddle • Sell call and put with same strike price • Profits when volatility is low • Potential unlimited loss from stock price changes in either direction

27. Butterfly Spreads • Insures against losses from a written straddle • Out-of-the-money put provides insurance on the downside • Out-of-the-money call provides insurance on the upside

28. Swaps • Contract for exchange of payments over time • Forward is single-payment swap • Multiple forwards, but as single transaction