Ch01-Introduction(金融工程學(xué),華東師大)

1、2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.1Financial Engineering金融工程學(xué) Textbook： John C. Hull, Options, Futures and Other Derivative Securities, Prentice Hall, 4th Ed.(清華大學(xué)出版社,) New Edition: 5th, 第三版中譯本：張?zhí)諅?，華夏出版社，2000 Hulls homepage: htpp:/ww

2、w.rotman.utoronto.ca/hull to download slides and software My homepage: /yctang2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.2References John C. Hull, Fundamentals of Futures and Options Markets, Prentice Hall, 4th Ed.,2002.(清華大學(xué)出版社)Robert W. Kol

3、b, Futures, Options and Swaps, Blackwell Publishing, 4th Ed., 2002.Lawrence Galitz, Financial Engineering: Tools and Techniques to Manage Financial Risks, Pitman Publishing, 1995. (中譯本：唐旭，經(jīng)濟(jì)科學(xué)出版社，1998） John F. Mrshall, Vipul K. Bansal, Financial Engineering, Simon & Schuster, 1992. (中譯本：宋逢明，朱寶憲，清華大學(xué)

4、出版社，1998） 李森，期權(quán)理論與案例分析：一個戰(zhàn)略性的投資，復(fù)旦大 學(xué)出版社，2002年8月. 張志強，期權(quán)理論與公司理財，華夏出版社，1999.2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.3IntroductionChapter 12021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.4

5、The Nature of DerivativesA derivative（衍生產(chǎn)品/工具） is an instrument whose value depends on the values of other more basic underlying（標(biāo)的/原生）variables2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.5Examples of DerivativesForward Contracts(遠(yuǎn)期合約)Futures

6、Contracts (期貨合約)Swaps(互換)Options（期權(quán)）2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.6Derivatives MarketsExchange (交易所)tradedTraditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic tradingContract

7、s are standard and there is virtually no credit riskOver-the-counter (OTC，場外市場)A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managersContracts can be non-standard and there is some small amount of credit risk2021/9/11Options, Futures, and Other

8、 Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.7Ways Derivatives are UsedTo hedge(規(guī)避) risksTo speculate(投機(jī)) (take a view on the future direction of the market)To lock in(鎖定) an arbitrage(套利) profitTo change the nature of a liability(負(fù)債)To change the nature of an investment without

9、incurring the costs of selling one portfolio(投資組合) and buying another2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.8Forward Contracts(遠(yuǎn)期合約)A forward contract is an agreement(協(xié)議) to buy or sell an asset at a certain time in the future for a certa

10、in price (the delivery price，交割價格)It can be contrasted with a spot contract (現(xiàn)貨合約)which is an agreement to buy or sell immediatelyIt is traded in the OTC market2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.9Foreign Exchange Quotes for GBP on Aug

11、 16, 2001 (See page 3)Bid(出價) Offer(報價)Spot1.44521.44561-month forward1.44351.44403-month forward1.44021.44076-month forward1.43531.435912-month forward1.42621.42682021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.10TerminologiesThe party that has a

12、greed to buy has what is termed a long position(多頭)The party that has agreed to sell has what is termed a short position(空頭)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.11Example (page 3)On August 16, 2001 the treasurer of a corporation enters

13、into(簽署) a long forward contract(多頭遠(yuǎn)期合約) to buy 1 million in six months at an exchange rate of 1.4359This obligates the corporation to pay $1,435,900 for 1 million on February 16, 2002What are the possible outcomes?2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTan

14、g Yincai, 20051.12Payoff(損益) from aLong Forward PositionProfit Price of Underlying at Maturity, STK2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.13Payoff from a Short Forward PositionProfitPrice of Underlying at Maturity, STK2021/9/11Options, Fu

15、tures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.14Futures Contracts (期貨合約)Agreement to buy or sell an asset for a certain price at a certain timeSimilar to forward contractWhereas a forward contract is traded OTC, a futures contract is traded on an exchange2021/9/11O

16、ptions, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.151. Gold: An Arbitrage Opportunity?Suppose that:The spot price of gold is US$300The 1-year forward price of gold is US$340The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity? 2021/9/

17、11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.162. Gold: Another Arbitrage Opportunity?Suppose that:The spot price of gold is US$300The 1-year forward price of gold is US$300The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity?

18、2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.17The Forward Price of Gold If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S (1+r )Twhere r is the 1-year (domestic currency) risk-free rate

19、 of interest.In our examples, S = 300, T = 1, and r =0.05 so thatF = 300(1+0.05) = 3152021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.181. Oil: An Arbitrage Opportunity?Suppose that:The spot price of oil is US$19The quoted 1-year futures price of

20、oil is US$25The 1-year US$ interest rate is 5% per annumThe storage costs of oil are 2% per annumIs there an arbitrage opportunity?2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.192. Oil: Another Arbitrage Opportunity?Suppose that:The spot price

21、of oil is US$19The quoted 1-year futures price of oil is US$16The 1-year US$ interest rate is 5% per annumThe storage costs of oil are 2% per annumIs there an arbitrage opportunity?2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.20Examples of Futu

22、res ContractsAgreement to:buy 100 oz. of gold US$300/oz. in December (COMEX) sell 62,500 1.5000 US$/ in March (CME)sell 1,000 bbl. of oil US$20/bbl. in April (NYMEX)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.21OptionsA call option(看漲期權(quán)) is an

23、 option to buy a certain asset by a certain date for a certain price (the strike price，執(zhí)行價格/敲定價格)A put option(看跌期權(quán)) is an option to sell a certain asset by a certain date for a certain price (the strike price)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yinc

24、ai, 20051.22An American options can be exercised at any time during its lifeA European option can be exercised only at maturity American vs European Options2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.23Examples: Cisco Options (May 8, 2000; Sto

25、ck Price=62.75)Strike PriceJuly CallOct CallJuly PutOct Put5016.8718.872.694.62657.0010.878.2510.62802.005.0017.5019.502021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.24Long Call on Microsoft (Figure 1.2, Page 7) Profit from buying a European(歐式)

26、call option on Microsoft: option price = $5, strike price = $603020100-530405060708090Profit ($)Terminalstock price ($)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.25Short Call on Microsoft (Figure 1.4, page 9) Profit from writing a European ca

27、ll option on Microsoft: option price = $5, strike price = $60-30-20-100530405060708090Profit ($)Terminalstock price ($)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.26Long Put on IBM (Figure 1.3, page 8) Profit from buying a European put option

28、on IBM: option price = $7, strike price = $903020100-790807060100110120Profit ($)Terminalstock price ($)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.27Short Put on IBM (Figure 1.5, page 9) Profit from writing a European put option on IBM: optio

29、n price = $7, strike price = $90-30-20-107090807060100110120Profit ($)Terminalstock price ($)2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.28Payoffs(損益) from OptionsWhat is the Option Position in Each Case? K = Strike price, ST = Price of asset

30、at maturityPayoffPayoffSTSTKKPayoffPayoffSTSTKK2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.29Options vs. Futures/ForwardsA futures/forward contract gives the holder the obligation to buy or sell at a certain priceAn option gives the holder the

31、 right to buy or sell at a certain price2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.30Types of Traders Hedgers(套期保值者) Speculators(投機(jī)者) Arbitrageurs(套利者)Some of the large trading losses in derivatives occurred because individuals who had a mand

32、ate(授權(quán)) to hedge risks switched to being speculators2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.31Hedging Examples A US company will pay 10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward co

33、ntract (The 3-month forward exchange rate is 1.6056). What are the alternative strategies?An investor owns 1,000 Microsoft shares currently worth $73 per share. A two-month put with a strike price of $65 costs $2.50. The investor decides to hedge by buying 10 contracts 2021/9/11Options, Futures, and

34、 Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.32Differences in the two hedge alternativesForward contracts are designed to neutralize risk by fixing the price that the hedger will pay or receive for the underlying asset. There is no assurance that the outcome with hedging is

35、 better than the outcome without hedging.The hedge using forward contract requires no initial payment 2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.33Option contracts provide assurance. They offer a way for investors to protect themselves agains

36、t adverse price movements in the future while still allowing them to benefit from favorable price movements.Option involve the payment of an up-front fee. 2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.34Speculation Example 1 An investor feels th

37、at sterling will strengthen relative to the U.S. dollar over the next two months. The current rate is 1.6470$/ and the 2-month futures price is 1.6410 $/ .What are the alternative strategies? 2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.35Two s

38、trategies:Buy 250,000 for $411,750, deposit the sterling in an interest-earning account for two months. Take a long position in 4 two-month futures contracts on sterling (each for 62,500).2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.36Possible

39、outcomesExchange rate is 1.7000 in two months. The investor makes $(1.7000-1.6470)x250,000=$13,250 using the first strategy and $(1.7000-1.6410) x250000=$14,750 using the second strategy. Exchange rate is 1.6000 in two month. The investor has a loss of $(1.6470-1.6000)x25000=$11,750 using the first

40、strategy and $(1.6410-1.6000)x25000 =$10,250 using the second strategy.2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.37Speculation Example 2 An investor with $4,000 to invest feels that the price of A will increase over the next 2 months. The cu

41、rrent stock price is $40 and the price of a 2-month call option with a strike of 45 is $2What are the alternative strategies? 2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.38Two strategies:Buy 100 shares of A.Buy 2,000 2-month call options (i.e.

42、 20 contracts) on A with a $45 strike price.The cost of each alternative is $4,000.2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 20051.39Possible outcomesA rises to $70 two months later. The Investor makes a profit of $100 x(70-40)=$3,000 using the fi

43、rst strategy and $2,000 x(70-45)-$2,000 x2=$46,000 using the second.A falls to $30 two months later. The investor losses $100 x(40-30)=$1,000 with the first strategy and $4,000 with the second strategy.2021/9/11Options, Futures, and Other Derivatives, 4th edition 2000 by John C. HullTang Yincai, 200

44、51.40A ComparisonBoth futures and options contracts provide a way in which a type of leverage can be obtained (compared with the spot market). Good outcomes becomes very good, while bad outcomes become very bad. In example1: the first alternative requires an up-front investment of $411,750 while the second alternative only requires a small amount say, $25,000 (deposited in a margin accoun