2. 1 Today Options Risk management: Why, how, and what? Option payoffs Reading Brealey and Myers, Chapter 20, 21

3. 2 Types of questions Your company, based in the U.S., supplies machine tools to manufacturers in Germany and Brazil. Prices are quoted in each country’s currency, so fluctuations in the € / $ and R / $ exchange rate have a big impact on the firm’s revenues. How can the firm hedge these risks? Should it? Your firm is thinking about issuing 10-year convertible bonds. In the past, the firm has issued straight debt with a yield-to-maturity of 8.2%. If the new bonds are convertible into 20 shares of stocks, per $1,000 face value, what interest rate will the firm have to pay on the bonds? Why? You have the opportunity to purchase a mine that contains 1 million kgs of copper. Copper has a price of $2.2 / kg, mining costs are $2 / kg, and you have the option to delay extraction one year. How much is the mine worth?

4. 3 Exchange rates, 1995 – 2003

5. 4 Example

6. 5 $ exchange rate, 1980 – 2000

7. 6 Risk management What is the goal? How can firms create value through risk management? View 1: Hedging is irrelevant (M&M) Purely financial transaction Diversified shareholders don’t care about firm-specific risks

8. 7 Risk management What is the goal? How can firms create value through risk management? View 2: Hedging creates value Reduces probability of financial distress Improves performance evaluation and compensation Other benefits: reduce taxes, undiversified shareholders

9. 8 Why hedge? Three gold producers Homestake Mining Does not hedge because “shareholders will achieve maximum benefit from such a policy.” American Barrick Hedges aggressively to give the company “extraordinary financial stability… offering investors a predictable, rising earnings profile in the future.” Battle Mountain Gold Hedges up to 25% because “a recent study indicates that there may be a premium for hedging.”

10. 9 Derivative use Evidence Random sample of 413 large firms Average cashflow from operations = $735 million Average PP&E = $454 million Average net income = $318 million How much hedging? 57% of firms use derivatives in 1997

11. 10 Financial derivatives

12. 11 Financial derivatives Assets Financial assets Stocks, bonds, stock indices, Tbonds (interest rates), foreign exchange Commodities Oil, gold, silver, corn, soybeans, OJ, pork bellies, coffee Other events and prices Electricity, weather, etc. Imbedded options Convertible bonds, warrants, real options, mortgages

13. 12 Futures contract On Thursday, 5 th May 2004, the NYM traded natural gas futures with delivery in August 2004 at a price of 4.900 $ / MMBtu. Buyer has a ‘long’ position Wins if prices go up Seller has a ‘short’ position Wins if prices go down The price of the contract is zero No cash changes hands today

14. 13 Futures contract: Payoff diagram

15. 14 Option Contract Contract between two parties Buy - Long Sell - Short For buyer: it is “right” rather than “obligation” Premium: the purchase price of the option Write a call option: option writer

16. 15 Option Contract Call option: the right to buy an asset at a specified exercise price (strike price) on or before a specified expiration date –February call option on Microsoft stock with exercise price $80. Put option: the right to sell an asset at a specified exercise price on or before a specified expiration date –February put option on IBM stock with exercise price $90.

17. 16 Option Contract Open interest: –The number of contracts currently outstanding Key Elements –Underlying asset –Exercise or Strike Price –Premium or Price –Maturity or Expiration

18. 17 Different Types of Options -by exercise timing American vs European Options –American: the option can be exercised at any time on or before the expiration or maturity date –European: the option can only be exercised on the expiration or maturity date

19. 18 Different Types of Options -by underlying asset Stock Options –Each option contract provides for the right to buy and sell 100 shares of stock in the US –Each option contract provides for the right to buy and sell 5,000 shares of stock in Taiwan Index Options: cash settlement Futures Options: –Foreign exchange futures options Foreign Currency Options Interest Rate Options: Treasury bills (bond)

20. 19 Payoffs and Profits on Options at Expiration - Calls Example –You buy an European Call, February Microsoft stock with x=$70 for $14 –Price on 2/28: 1) $90 2) $80 3) $70 4) $60 –What is your payoff? –What is your profit?

21. 20

22. 21 Payoffs and Profits on Options at Expiration - Calls Notation Stock Spot Price = S T ， Exercise Price = X Payoff to Call Holder (S T - X) if S T >X 0 if S T < X Profit to Call Holder =Payoff - Purchase Price (premium)

23. 22 Payoffs and Profits on Options at Expiration - Calls Payoff to Call Writer - ( S T - X) if S T >X 0if S T < X Profit to Call Writer =Payoff + Premium

24. 23 Payoff Stock Price 0 Call Writer Call Holder Payoff Profiles for Calls

25. 24 Profit Stock Price 0 Call Writer Call Holder Profit Profiles for Calls

26. 25 Payoffs and Profits at Expiration - Puts Example –You buy an European Put, February IBM stock with x=$90 for $15 –Price on 2/28: 1) $60 2) $80 3) $90 4) $100 –What is your payoff? –What is your profit?

27. 26

28. 27 Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0if S T > X (X - S T ) if S T < X Profit to Put Holder Payoff - Premium

29. 28 Payoffs and Profits at Expiration - Puts Payoffs to Put Writer 0if S T > X -(X - S T )if S T < X Profits to Put Writer Payoff + Premium

30. 29 Payoff Profiles for Puts 0 Payoff Stock Price Put Writer Put Holder

31. 30 Profit Profiles for Puts 0 Profits Stock Price Put Writer Put Holder

32. 31 Market and Exercise Price Relationships In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable Call: market price < exercise price Put: exercise price < market price At the Money - exercise price and asset price are equal

33. 32 Option-like Securities Callable Bonds Issuer hold a call option Convertible Bonds Bond holders long a call Warrants An option issued by a firm. When exercised, number of shares outstanding will increase and there are cash inflows to the firm.

34. 33 WSJ option quotes

35. 34 Option payoffs (strike = $50)

36. 35 Options

37. 36 Returns, stock vs. option

38. 37 Option strategies Financial engineering Options can be mixed in various ways to create an unlimited number of payoff profiles. Examples Buy a stock and a put Buy a call with one strike price and sell a call with another Buy a call and a put with the same strike price

39. 38 Option strategies: Stock + put

40. 39 Option strategies: Call1 – call2

41. 40 Option strategies: Call + Put

42. 41 Option Strategies Straddle When a stock will move a lot in price but are uncertain about the direction of the move Long straddle : Buy both a call and a put on a stock, each with the same exercise price and the same expiration date Write straddle: Sell both a call and a put on a stock, each with the same exercise price and the same expiration date

43. 42 多頭跨式部位 採取多頭跨式部位的原因在於未來標的物價格的 波動太大，投資人無法判斷標的物價格的趨勢， 因此採取多頭跨式部位，當標的物價格有劇烈波 動時，將可獲得利潤。 買進買權 買進賣權 STST 多頭跨式部位 K

44. 43 空頭跨式部位 空頭跨式部位則是投資人同時賣出到期日期和 履約價格相同的買權與賣權所組成的。 STST 賣出賣權 賣出買權 放空跨式部位 K

45. 44 股價指數選擇權 股價指數選擇權（ Stock-Index Option ）之標的 物為股價指數，不同於股票選擇權，履約時採 現金交割的方式。

46. 45 Index-Options 台指選擇權 (TXO) Buy a call X=5700 ， C=400 點 Multiplier( 契約乘數 =50 元 ) 到期 :TXO=6200 權利金 :400 x $50=20,000 Payoff:(6200-5700)x50=25,000 Profit ( 利得 ):$25,000-20,000=5,000

47. 46 Index-Options: Risk Management Portfolio:P V p =5 million, β p =1, when Index=250 Buy 200 index put option (each put:100 multiplier) X=235 I T =225 ， Vp=5*(225/250)=4.5 million ﹝ 100x(235-225) ﹞ x 200 =200,000=0.2 million Total loss:5-(4.5+0.2)=0.3 million