1. Derivatives Workshop Actuarial Society October 30, 2007

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

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

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

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

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

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

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

9. Example Stock price now = $50 Stock price now = $50 Stock price one year from now = $49.50 Stock price one year from now = $49.50 Commission = $1/transaction Commission = $1/transaction How much can you make short selling 100 shares? How much can you make short selling 100 shares? Profit = $50*100-$49.50*100-$2 = $48 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 Sets terms now for the buying or selling of an asset at specified time in future Specifies quantity and type of asset Specifies quantity and type of asset Sets price to be paid (forward price) Sets price to be paid (forward price) Obligates seller to sell and buyer to buy Obligates seller to sell and buyer to buy Settles on expiration date Settles on expiration date

11. Forward Contracts Forward price -- price to be paid Forward price -- price to be paid Spot price -- market price now Spot price -- market price now Underlying asset -- asset on which contract is based Underlying asset -- asset on which contract is based Buyer = long; Seller = short Buyer = long; Seller = short Long position makes money when price Long position makes money when price Short 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 Payoff to long forward (buyer) = Spot price at expiration - forward price Agreed to buy at fixed (forward) price Agreed to buy at fixed (forward) price Payoff to short forward (seller) = Forward price - spot price at expiration Payoff to short forward (seller) = Forward price - spot price at expiration Agreed to sell at fixed price Agreed to sell at fixed price

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

14. Call Options Strike price - amount buyer pays for the asset Strike price - amount buyer pays for the asset Exercise - act of paying strike price to receive the asset Exercise - act of paying strike price to receive the asset Expiration - when option must be exercised, or become worthless Expiration - when option must be exercised, or become worthless European style - only exercise on x-date European style - only exercise on x-date Bermudan style - during specified periods Bermudan style - during specified periods American style - entire life of option 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 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] Purchased call payoff = max[0, spot price at x-date - strike price] Must pay premium to seller Must pay premium to seller Profit = payoff - future value of premium Profit = payoff - future value of premium

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

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

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

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

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

21. Put-Call Parity No arbitrage No arbitrage Net cost of index must be same whether through options or forward contract Net cost of index must be same whether through options or forward contract Call (K,T) – Put(K,T) = PV(F 0, T – K)

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

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

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

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

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

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

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