金融衍生工具市場(chǎng)

1、2金融衍生工具市場(chǎng)的作用金融衍生工具市場(chǎng)的作用 Private contract between 2 partiesExchange tradedNon-standard contractStandard contractUsually 1 specified delivery dateRange of delivery datesSettled at end of contractSettled dailyDelivery or final cashsettlement usually occursContract usually closed outprior to maturityFUT

2、URESSome credit riskVirtually no credit risk Available on a wide range of underlyings Exchange traded Specifications need to be defined: What can be delivered, Where it can be delivered, & When it can be delivered Settled daily Available on a wide range of underlyings Exchange traded Specifications

3、need to be defined: What can be delivered, Where it can be delivered, & When it can be delivered Settled dailyMarginsA Possible OutcomeTable 2.1, Page 28 DailyCumulativeMarginFuturesGainGainAccountMarginPrice(Loss)(Loss)BalanceCallDay(US$)(US$)(US$)(US$)(US$)400.004,0005-Jun 397.00(600) (600) 3,4000

4、.13-Jun 393.30(420) (1,340) 2,6601,340 .19-Jun 387.00(1,140) (2,600) 2,7401,260 .26-Jun 392.30260 (1,540) 5,0600+=4,0003,000+=4,000一位投資折簽訂了兩份冷凍橙汁的多頭期貨合約，每份合約的交割數(shù)量都為15,000磅。當(dāng)前期貨價(jià)格為每磅160美分；每份合約的初始保證金為$6,000;維持保證金都為$4,500。價(jià)格如何變化會(huì)導(dǎo)致保證金催付？在什么情況下，可以從保證金賬戶中提回$2,000? 3020100-5708090100110 120 130Profit ($)T

5、erminalstock price ($)-30-20-1005708090100110 120 130Profit ($)Terminalstock price ($)3020100-7706050408090100Profit ($)Terminalstock price ($)-30-20-1070706050408090100Profit ($)Terminalstock price ($)PayoffKSTSTKPayoffPayoffSTSTKKPayoffStocksForeign CurrencyStock IndicesFuturesSpecification ofExch

6、ange-Traded Options假設(shè)一個(gè)執(zhí)行價(jià)格為$50的歐式看漲期權(quán)價(jià)值$2.50,并持有到期。在何種情況下期權(quán)的持有者會(huì)有盈利？在何種情況下，期權(quán)會(huì)被執(zhí)行？請(qǐng)畫圖說(shuō)明期權(quán)的多頭方的收益是如何隨期權(quán)到期日的股價(jià)的變化而變化的。 假設(shè)一歐式看跌期權(quán)執(zhí)行價(jià)格為$60，價(jià)值為$4.00并持有到期。在何種情況下，期權(quán)持有者（即空頭方）會(huì)有盈利？在何種情況下，期權(quán)會(huì)被執(zhí)行？請(qǐng)畫圖說(shuō)明期權(quán)的空頭方的收益是如何隨期權(quán)到期日的股價(jià)的變化而變化的。It is May and a trader writes a September call option with a strike price of $2

7、0.The stock price is $18 and the option price is $2. Describe the traders cash flows if the option is held until September and the stock price is $25 at that time.一位投資者出售了一個(gè)歐式12月份到期的看跌期權(quán)，執(zhí)行價(jià)格為$30,期權(quán)價(jià)值為$4。在什么情況下，投資者會(huì)有盈利？一種股票的現(xiàn)價(jià)為$94,執(zhí)行價(jià)格為$95的3個(gè)月期的看漲期權(quán)價(jià)格為$4.70。一位投資者預(yù)計(jì)股票價(jià)格將要上升，正在猶豫是購(gòu)買100股股票，還是購(gòu)買20份看漲期權(quán)（

8、每份合約為100股）。兩種策略都須投資$9,400。你會(huì)給他什么建議？股票價(jià)格上升到多少時(shí)，購(gòu)買期權(quán)會(huì)盈利更大？1.我國(guó)某外貿(mào)公司3月1日預(yù)計(jì)3個(gè)月后用美元支付400萬(wàn)英鎊進(jìn)口貨款，預(yù)測(cè)英鎊匯價(jià)會(huì)有大幅度波動(dòng)，以貨幣期權(quán)交易保值。已知：3月1日即期匯價(jià)GBP1=USD1.4865(IMM)協(xié)定價(jià)格GBP1=USD1.4950(IMM)期權(quán)費(fèi)GBP1=USD0.0212期權(quán)交易傭金占合同金額的0.5%，采用歐式期權(quán)。3個(gè)月后假設(shè)美元市場(chǎng)匯價(jià)分別為GBP1=USD1.4000與GBP1=USD1.6000，問(wèn)該公司各需支付多少美元？2.我國(guó)某外貿(mào)公司向英國(guó)出口商品，6月2日裝船發(fā)貨，收到價(jià)值100

9、萬(wàn)英鎊的3個(gè)月遠(yuǎn)期匯票，擔(dān)心到期結(jié)匯時(shí)英鎊對(duì)美元匯價(jià)下跌，減少美元匯價(jià)收入，以外匯期權(quán)交易保值。已知：6月2日即期匯價(jià)GBP1=USD1.4500（IMM)協(xié)定價(jià)格GBP1=USD1.4800（IMM)期權(quán)費(fèi)GBP1=USD0.0212期權(quán)交易傭金占合同金額的0.5%，采用歐式期權(quán)。3個(gè)月后在英鎊對(duì)美元匯價(jià)分別為GBP1=USD1.4000與GBP1=USD1.6000兩種情況下，該公司各收入多少美元？133股票價(jià)格指數(shù)期權(quán)交易股票價(jià)格指數(shù)期權(quán)交易 cpCPVariableS0KTrD+?+American vs European OptionsAn American option is wo

10、rth at least as much as the corresponding European optionC cP pConversion Formulas(Page 79)DefineRc : continuously compounded rateRm: same rate with compounding m times per yearRmRmRm ecmmRmcln/11A 3-month call option on the stock has a strike price of 21. A stock price is currently $20 In three mon

11、ths it will be either $22 or $18Stock Price = $22Stock Price = $18Stock price = $20Stock Price = $22Option Price = $1Stock Price = $18Option Price = $0Stock price = $20Option Price=?A Call OptionA 3-month call option on the stock has a strike price of 21. Consider the Portfolio:long D sharesshort 1

12、call option Portfolio is riskless when 22D 1 = 18D or D = 0.2522D 118DSetting Up a Riskless PortfolioValuing the Portfolio(Risk-Free Rate is 12%) The riskless portfolio is: long 0.25 sharesshort 1 call option The value of the portfolio in 3 months is 22 0.25 1 = 4.50 The value of the portfolio today

13、 is 4.5e 0.120.25 = 4.3670 The riskless portfolio is: long 0.25 sharesshort 1 call option The value of the portfolio in 3 months is 22 0.25 1 = 4.50 The value of the portfolio today is 4.5e 0.120.25 = 4.3670Valuing the Option The portfolio that is long 0.25 sharesshort 1 option is worth 4.367 The va

14、lue of the shares is 5.000 (= 0.25 20 ) The value of the option is therefore 0.633 (= 5.000 4.367 )Generalization (Figure 11.2, page 243)A derivative lasts for time T and is dependent on a stockS0u uS0d dS0Generalization(continued) Consider the portfolio that is long D shares and short 1 derivative

15、The portfolio is riskless when S0uD u = S0dD d ordSuSfdu00DS0uD uS0dD dGeneralization(continued) Value of the portfolio at time T is S0uD u Value of the portfolio today is (S0uD u)erT Another expression for the portfolio value today is S0D f Hence = S0D (S0uD u )erT Generalization(continued) Substit

16、uting for D we obtain = pu + (1 p)d erTwhere pedudrTp as a Probability It is natural to interpret p and 1-p as probabilities of up and down movements The value of a derivative is then its expected payoff in a risk-neutral world discounted at the risk-free rateS0u uS0d dS0p(1 p )Risk-neutral Valuatio

17、n When the probability of an up and down movements are p and 1-p the expected stock price at time T is S0erT This shows that the stock price earns the risk-free rate Binomial trees illustrate the general result that to value a derivative we can assume that the expected return on the underlying asset

18、 is the risk-free rate and discount at the risk-free rate This is known as using risk-neutral valuationOriginal Example RevisitedSince p is the probability that gives a return on the stock equal to the risk-free rate. We can find it from20e0.12 0.25 = 22p + 18(1 p )which gives p = 0.6523Alternativel

19、y, we can use the formula6523.09 .01 .19 .00.250.12edudeprTS0u = 22 u = 1S0d = 18 d = 0S0 p(1 p )Valuing the Option Using Risk-Neutral ValuationThe value of the option is e0.120.25 (0.65231 + 0.34770) = 0.633S0u = 22 u = 1S0d = 18 d = 0S00.65230.3477 Suppose that are the prices of European call opti

20、ons with strike prices respectively, where and All options have the same maturity. Show that 123ccc、123X、XX321XXX3221XXXX2130.5()ccc5.4.4其他類型衍生金融工具市場(chǎng) 1互換交易（Swap） 它是指兩個(gè)或兩個(gè)以上當(dāng)事人在約定的時(shí)間內(nèi)，按預(yù)定條件交換一系列支付款項(xiàng)的金融交易?；Q交易最基本的類型是貨幣互換(Currency Swap)和利率互換(Interest Rate Swap)。 1）貨幣互換。它是指當(dāng)兩個(gè)籌款人各自借取的貨幣不同，但金額等值、期限相同時(shí)，按照

21、約定的條件，互相償付對(duì)方到期應(yīng)償付的本息。 LIBOR+3.5%的浮動(dòng)利率 A公司 B公司 付12% LIBOR+3.5% 13.5%的固定利率 放款人 放款人A公司與公司與B公司進(jìn)行利率互換后，各自的借公司進(jìn)行利率互換后，各自的借款成本見(jiàn)表款成本見(jiàn)表6-1： A公司 B公司 支付給第三方貸款人 +12% +(LIBOR+3.5%) 支付給對(duì)方 +(LIBOR+3.5%) +13.5% 從對(duì)方收到 -13.5% -(LIBOR+3.5%) 籌資總成本 LIBOR+2% 13.5% 不安排互換時(shí)的籌資成本 LIBOR+2.5% 14% 凈節(jié)約成本 0.5% 0.5% An Example of

22、a “Plain Vanilla” Interest Rate Swap An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows-Millions of Dollars-LIBORFLOATING FIXED NetDateRateCash Flow Cash Flow Cash

23、FlowMar.5, 20044.2%Sept. 5, 20044.8%+2.102.500.40Mar.5, 20055.3%+2.402.500.10Sept. 5, 20055.5%+2.652.50+0.15Mar.5, 20065.6%+2.752.50+0.25Sept. 5, 20065.9%+2.802.50+0.30Mar.5, 20076.4%+2.952.50+0.45Cash Flows to Microsoft(See Table 7.1, page 151)Typical Uses of anInterest Rate Swap Converting a liability fromfixed rate to floating rate floating rate to fixed rate Converting an investment from fixed rate to floating ratefloating rate to fixed rate Intel and Microsoft (MS) Transform a Liability(Figure 7.2, page 152)IntelMSLIBOR5%LIBOR+0.1%5.2%Financial In