第講用于匯率風(fēng)險(xiǎn)管理的衍生產(chǎn)品貨幣期貨與期貨市場(chǎng)

1、 chapter 2 derivative securities for currency risk management currency futures and futures markets chapter overviewn1financial futures exchangesn2the operation of futures marketsn3futures contractsn4forward versus futures market hedgesn5futures hedges using cross exchange ratesn6hedging with currenc

2、y futures chapter objectivesnthis chapter compares currency futures contracts to currency forward contracts and shows how they are priced by the marketplace. -emphasis is placed on how currency futures contracts are similar to, and yet different from, forward contracts. nthe last several sections di

3、scuss implementation issues:-delta hedges for maturity mismatches-cross hedges for currency mismatches-delta-cross hedges for currency and maturity mismatches forward market1. forward contractsa forward contract is an agreement between a corporation and a commercial bank to exchange a specified amou

4、nt of a currency at a specified exchange rate (called the forward rate) and on a specified future date.when mncs anticipate a future need for or future receipt of a foreign currency, they can set up forward contracts to lock in the rate at which they can purchase or sell a particular foreign currenc

5、y. a forward hedge of the dollarunderlying position of afrench exporter (long $s)sell $s forward at ft/$(short $s and long s)net position+$40 million+40 million -$40 million+40 million-goodsv/$long $ss/$short $sthe forward contract provides a perfect hedge because the size and timing of the hedge tr

6、ansaction exactly offsets the size and timing of the underlying exposure. forward market2. non-deliverable forward contractsa. new typena non-deliverable forward contract (ndf) does not result in an actual exchange of currencies. instead, one party makes a net payment to the other based on a market

7、exchange rate on the day of settlement.b. frequently used for currency in emerging marketsc. no delivery requiredd. one party to the agreement makes a payment to the other party based on the exchange rate at the future date. nan ndf can effectively hedge future foreign currency payments or receipts:

8、 ndf marketexpect need for 100m chilean pesos. negotiate an ndf to buy 100m chilean pesos on jul 1. reference index (closing rate quoted by chiles central bank) = $.0020/peso.april 1buy 100m chilean pesos from market.july 1index = $.0023/peso receive $30,000 from bank due to ndf. index = $.0018/peso

9、 pay $20,000 to bank. forward versus futures contractsn comparing currency futures contracts to currency forward contracts and shows how they are priced by the marketplace. nforwards are a pure credit instrumentqwhichever way the price of the spot rate of exchange moves, one party always has an ince

10、ntive to default(違約動(dòng)機(jī)）違約動(dòng)機(jī)）eg,fx,$1.475/,當(dāng)匯率上升時(shí)，賣(mài)方有違約動(dòng)機(jī)，當(dāng)匯率下降時(shí)，買(mǎi)方有違約動(dòng)機(jī)。nthe futures contract solutionqa futures exchange clearinghouse takes one side of every transaction (and makes sure that its exposures cancel one another)qcontracts are marked-to-market daily qrequire initial and maintenance marg

11、ins forwards versus futuresforwardsfuturescounterpartybankcme clearinghouse（forward contracts are created by commercial and investment banks, whereas futures contracts are usually found on futures exchanges）maturitynegotiated3rd week of the month (us)amountnegotiatedstandard contract sizefeesbid-ask

12、commissionscollateralnegotiatedmargin accountsettlementat maturitymost are settled earlyfutures exchangesnfinancial futures exchanges are usually associated with a commodity futures exchange2002 volumetop 5 futures exchanges(million contracts)eurex - eurex (germany & switzerland)536.0cme - chica

13、go mercantile exchange (u.s.)444.5cbot - chicago board of trade (u.k.)276.3euronext - (amsterdam, brussels, lisbon, paris, london)221.3nymex - new york mercantile exchange (u.s.)107.4bm&f - bolsa mercadorias & de futuros (brazil) 95.9source: futures industry association forwards versus futur

14、esnfutures contracts are similar to forward contractsqfutures contracts are like a bundle of consecutive one-day forward contracts（期貨合約是一連串可更新的（期貨合約是一連串可更新的1天期遠(yuǎn)期合約的組合：天期遠(yuǎn)期合約的組合： each day, the previous days forward contract is replaced by a new one-day forward contract with a delivery price equal to

15、the closing price from the previous days contract. 如三個(gè)月期的遠(yuǎn)期合約，相當(dāng)于如三個(gè)月期的遠(yuǎn)期合約，相當(dāng)于90個(gè)可更新的個(gè)可更新的1天期的遠(yuǎn)期合約天期的遠(yuǎn)期合約qdaily settlement is the biggest difference between a forward and a futures contractnfutures and forwards are nearly identical in their ability to hedge risk（在規(guī)避風(fēng)險(xiǎn)管理的功能上有相似之處）（在規(guī)避風(fēng)險(xiǎn)管理的功能上有相似之處）

16、hedging with futuresnforward contracts can be tailored to match the underlying exposureforward contracts thus can provide a perfect hedge of transaction exposure to currency risknexchange-traded futures contracts are standardizedthey will not provide a perfect hedge if they do not match the underlyi

17、ng exposures currency mismatch - there may not be a futures contract in the currency that you would like to hedgematurity mismatch - there may not be a futures contract expiring on the same day as your underlying transaction exposurecontract size mismatch - the underlying transaction exposure may no

18、t be an even increment of existing futures contracts interest rate parity revisitednsome definitionsst,td/f = spot price at time t for expiry at time tft,td/f = forward price at time t for expiry at time tfutt,td/f = futures price at time t for expiry at time tnforward and futures prices are equal t

19、hrough interest rate parityninterest rate parity is usually expressed as a forward-looking relation from time zero to time t. (ftd/f / s0d/f) = (1+id)/(1+if)tnin the slide, irp is expressed as a backward-looking relation from time t through the expiration date t（即根據(jù)（即根據(jù)irp可以預(yù)測(cè)遠(yuǎn)期和期貨價(jià)格）可以預(yù)測(cè)遠(yuǎn)期和期貨價(jià)格）fut

20、t,td/f = ft,td/f = std/f (1+id)/(1+if)t- -t std/f (as t t)spot and futures price convergence at expiration t forward premium futtd/f = std/f fut0d/f s0d/f futures prices converge to spot prices at expiration.maturity mismatches and basis risknif there is a maturity mismatch, futures contracts may no

21、t provide a perfect hedgenbecause the convergence of futures prices to spot prices is nearly linear, interest rate differentials (1+id )/(1+if ) are often approximated by the simple difference in nominal interest rates, (id-if). nthe difference (id-if) is called the basisqthe risk of change in the r

22、elation between futures and spot prices is called basis riskqwhen there is a maturity mismatch, basis risk makes a futures hedge slightly riskier than a forward hedge（當(dāng)存在（當(dāng)存在期限錯(cuò)配時(shí)，基差風(fēng)險(xiǎn)使期貨套期保值相對(duì)遠(yuǎn)期套期技術(shù)而期限錯(cuò)配時(shí)，基差風(fēng)險(xiǎn)使期貨套期保值相對(duì)遠(yuǎn)期套期技術(shù)而言更有風(fēng)險(xiǎn)。）言更有風(fēng)險(xiǎn)。）maturity mismatches and delta hedgesnfutures hedge is called

23、 a delta hedge when there is a mismatch between the maturity (but not the currency) of a futures contract and the underlying exposure.nwhen there is a maturity mismatch, a futures hedge cannot provide a perfect hedge against currency risk.dec 16oct 26mar 13-s$10millionunderlying obligationfutures ex

24、piration date following the cash flowan example of a delta hedgetime 0time t=227/365sept 11futures expiration date following the cash flowtime t=278/365an example of a delta hedgenthere are 227days between march 13 and october 26.na hedge with the futures contract expires on september 11 only hedges

25、 against currency risk through that date. it remains exposed to changes in currency values from the end of the contract through october 26.nthe december futures contract is a better choice because it can hedge currency risk through october 26 and then be sold.nsuppose the spot rate is s0$/s$0.6010/s

26、$ on march 13, annual interest rate in the united states and singapore are i$6.24% and is$4.04%naccording to irp，the forward price for exchange on october 26 is f0,t$/s$ = s0$/s$ (1+i$)/(1+is$)t (0.6010)(1+6.24%)/(1+4.04%)227/365=$0.6089/s$nit can form a perfect hedge with a long forward contract fo

27、r delivery of s$10 million on october 26 in exchange for （$0.6089/s$)(s$10,000,000)=$6,089,000.as we shall see, the futures hedge using the december 16 futures contract is not quite as precise.an example of a delta hedgen該公司利用期貨合約套期該公司利用期貨合約套期3月月13日日買(mǎi)進(jìn)買(mǎi)進(jìn)12月到期的期貨合約，并月到期的期貨合約，并在在10月月26日賣(mài)出該期貨合約，風(fēng)險(xiǎn)在于日賣(mài)出

28、該期貨合約，風(fēng)險(xiǎn)在于12月到期的期貨合約運(yùn)行到月到期的期貨合約運(yùn)行到10月月26日時(shí)的價(jià)格如何變化？即期貨平倉(cāng)時(shí)的價(jià)格是多少？日時(shí)的價(jià)格如何變化？即期貨平倉(cāng)時(shí)的價(jià)格是多少？n3月月13日，日，12月到期的期貨合約價(jià)格：月到期的期貨合約價(jià)格：fut0,t$/s$ = s0$/s$ (1+i$)/(1+is$)t (0.6010)(1+6.24%)/(1+4.04%)278/365=$0.6107/s$（以此價(jià)格買(mǎi)入）（以此價(jià)格買(mǎi)入）n同時(shí)，根據(jù)遠(yuǎn)期匯率預(yù)測(cè)法，同時(shí)，根據(jù)遠(yuǎn)期匯率預(yù)測(cè)法，10月月26日的即期匯率是：日的即期匯率是： es0，t$/s$ = f0,t$/s$ =$0.6089/s$t

29、his expectation will hold only if interest rates, (1+i$)/(1+is$)=1.0624/1.0404=1.02115, remains constant, this ratio is the “basis” for changes in futures prices over time 10月月26日債務(wù)到期時(shí)，分三種情況討論：日債務(wù)到期時(shí)，分三種情況討論：情況一：基差不變：情況一：基差不變：basis i$-s$=6.24%-4.04%=2.20%,因此，因此，10月月26日的即期匯率不變，即日的即期匯率不變，即st$/s$ =$0.6

30、089/s$，在，在10月月26日，到日，到12月月16日交割的期貨合約價(jià)格就建立在之前預(yù)期的即期匯率日交割的期貨合約價(jià)格就建立在之前預(yù)期的即期匯率: st$/s$ =$0.6089/s$的基礎(chǔ)上，期限的基礎(chǔ)上，期限t-t27822751天：天： futt,t$/s$ = st$/s$ (1+i$)/(1+is$)t-t (0.6089)(1+6.24%)/(1+4.04%)51/365=$0.6107/s$（ 以此價(jià)格賣(mài)出）以此價(jià)格賣(mài)出）profit on futures: futt,t$/s$ - fut0,t$/s$ =$0.6107/s$-$0.6107/s$=0profit on u

31、nderlying short position in the spot currency: -(st$/s$ - est$/s$ )=-(=$0.6089/s$- $0.6089/s$=0情況二：情況二：10月月26日，新加坡利率上升至：日，新加坡利率上升至： is$=4.54%，導(dǎo)致，導(dǎo)致新元匯率新元匯率上升至：上升至： st$/s$ =$0.6255/s$因此，在因此，在10月月26日，到日，到12月月16日交割的期貨合約價(jià)格就變?yōu)椋喝战桓畹钠谪浐霞s價(jià)格就變?yōu)椋?futt,t$/s$ = st$/s$ (1+i$)/(1+is$)t-t (0.6255)(1+6.24%)/(1+4.54

32、%)51/365=$0.6269/s$（以此價(jià)格賣(mài)出）（以此價(jià)格賣(mài)出）此時(shí)，公司在期貨市場(chǎng)的收益為：此時(shí)，公司在期貨市場(chǎng)的收益為：profit on futures: futt,t$/s$ - fut0,t$/s$ =$0.6269/s$0.6107/s$=$0.0162/s$新元升值帶來(lái)的債務(wù)成本增加，即現(xiàn)貨市場(chǎng)公司損失為：新元升值帶來(lái)的債務(wù)成本增加，即現(xiàn)貨市場(chǎng)公司損失為：loss on underlying short position in the spot currency: -(st$/s$ - est$/s$ )=-($0.6255/s$- $0.6089/s$=-$0.0166/

33、s$凈損失凈損失+0.01620.0166$0.0004/s$，損失總額為：，損失總額為：$4000（總（總債務(wù)支出是債務(wù)支出是10百萬(wàn)）百萬(wàn)）損失增加是因?yàn)樾录悠吕噬仙?，基差改變所致。損失增加是因?yàn)樾录悠吕噬仙?，基差改變所致。情況三：情況三：10月月26日，美元利率上升至：日，美元利率上升至： i$=6.74%，導(dǎo)致，導(dǎo)致新元匯率貶值至：新元匯率貶值至： st$/s$ =$0.5774/s$因此，在因此，在10月月26日，到日，到12月月16日交割的期貨合約價(jià)格就變?yōu)椋喝战桓畹钠谪浐霞s價(jià)格就變?yōu)椋?futt,t$/s$ = st$/s$ (1+i$)/(1+is$)t-t (0.5774

34、)(1+6.74%)/(1+4.04%)51/365=$0.5795/s$（以此價(jià)格賣(mài)出）（以此價(jià)格賣(mài)出）此時(shí)，公司在期貨市場(chǎng)的損失為：此時(shí)，公司在期貨市場(chǎng)的損失為：profit on futures: futt,t$/s$ - fut0,t$/s$ =$0.5795/s$-$0.6107/s$ =$0.0312/s$由于新元貶值，公司債務(wù)成本節(jié)約，即公司收益為：由于新元貶值，公司債務(wù)成本節(jié)約，即公司收益為：loss on underlying short position in the spot currency: -(st$/s$ - est$/s$ )=-($0.5774/s$- $0.

35、6089/s$=+$0.0315/s$凈收益凈收益 $0.0312/s$ +$0.0315/s$ +$0.0003/s$，收益總額為：，收益總額為：$3000所得增加是因?yàn)樾录悠吕噬仙?，基差改變所致。所得增加是因?yàn)樾录悠吕噬仙?，基差改變所致。但總的?lái)講，但總的來(lái)講，futures contracts can provide very good hedge, because basis risk is small relative to currency risk. contract size mismatch and the hedge ratiothe forward hedge: th

36、e hedge ratio nf*of a future position is defined as nf*=amount in forward position/amount exposed to currency risk=-1the futures hedge: 是指保值者持有期貨合約的頭寸規(guī)模與需要保值是指保值者持有期貨合約的頭寸規(guī)模與需要保值的基礎(chǔ)資產(chǎn)之間的比率。的基礎(chǔ)資產(chǎn)之間的比率。 the hedge ratio is used to minimize the variance of the hedged position.即期匯率變化率與期貨匯率變化率的關(guān)系如下：即期匯率變化

37、率與期貨匯率變化率的關(guān)系如下：std/f = a a + b b futtd/f + etstd/f=percentage change in the spot ratefuttd/f= percentage change in the futures price std/f = (std/f-st-1d/f)/st-1d/f and futtd/f = (futtd/f-futt-1d/f)/futt-1d/f this regression is designed to estimate basis risk over the maturity of a proposed hedge.th

38、e slope coefficient b b = r rs,fut (s ss / s sfut ) measures the sensitivity of spot to futures pricesn)/(.futsfutsssrbfuttd/fstd/f)/()/()(.2,futsfutsfutfutsssrssbnfut*=(amount in futures)/(amount exposed) =-b b （通過(guò)歷史（通過(guò)歷史數(shù)據(jù)對(duì)上式回歸可以得出數(shù)據(jù)對(duì)上式回歸可以得出b b ）nhedge quality （對(duì)沖質(zhì)量）（對(duì)沖質(zhì)量）is measured by the r-squ

39、are (r2 = r rs,fut2). -r2 (or r rs,fut2) measures the percentage variation in std/f explained by variation in futtd/f.-high r2 low basis risk and a high-quality hedge. -low r2 high basis risk and a relatively poor hedge. r-square取值在（取值在（0，1）之間）之間contract size mismatch and the hedge ratiocontract siz

40、e mismatch and the hedge ratio假設(shè)假設(shè)b b1.0251.025，則期貨套期保值比率：，則期貨套期保值比率： nfut*=(amount in futures)/(amount exposed) =-b b -1.025 -1.025 amount in futures （-1.025）（）（ amount exposed）如上例中，該公式有如上例中，該公式有10001000萬(wàn)新元的空頭，需要持有的期貨多頭為萬(wàn)新元的空頭，需要持有的期貨多頭為 amount in futures （-1.025）（ -10000000） s$10,250,000芝加哥商品期貨交易所

41、一份新元期貨合約金額為芝加哥商品期貨交易所一份新元期貨合約金額為125,000125,000，所以，所以，持有期貨合約的規(guī)模為持有期貨合約的規(guī)模為82 82 份期貨合約份期貨合約:10,250,000/125,00082:10,250,000/125,00082an example of a hedge rationit is now january 8. you need to hedge a 100 million obligation due on june 3. qthe spot exchange rate is s0$/ = $1.10/qa 100,000 cme euro fu

42、tures contract expires on june 16qbased on st$/ = a a + b b futt$/ + et , you estimate b b = 1.020 with r2 = 0.95.(the relatively high r2 (0.95) of this regression means that this is a relatively high quality hedge. )qhow many cme futures contracts should you buy to minimize the risk of your hedged

43、position?the hedge ratio solutionnthe optimal hedge ratio for this delta hedge is given bynfut* =(amount in futures)/(amount exposed) = -b(amount in futures) = (-b)(amount exposed) = (-1.020)(-100 million) = 102 millionor (102 million) / (100,000/contract) = 1,020 contractscurrency mismatches and cr

44、oss hedgesa cross hedge is used when there is a maturity match but a currency mismatch即選擇的期貨避險(xiǎn)合約標(biāo)的商品與現(xiàn)貨商品不同，市場(chǎng)上沒(méi)有類(lèi)似現(xiàn)貨即選擇的期貨避險(xiǎn)合約標(biāo)的商品與現(xiàn)貨商品不同，市場(chǎng)上沒(méi)有類(lèi)似現(xiàn)貨所發(fā)行的期貨來(lái)避險(xiǎn)時(shí)，就要找另一個(gè)現(xiàn)貨價(jià)格有正相關(guān)，或者是同所發(fā)行的期貨來(lái)避險(xiǎn)時(shí)，就要找另一個(gè)現(xiàn)貨價(jià)格有正相關(guān)，或者是同質(zhì)的產(chǎn)品來(lái)避險(xiǎn)。質(zhì)的產(chǎn)品來(lái)避險(xiǎn)。例如，一家英國(guó)公司有加元債務(wù)，可以利用美元期貨的多頭來(lái)規(guī)避匯率例如，一家英國(guó)公司有加元債務(wù)，可以利用美元期貨的多頭來(lái)規(guī)避匯率風(fēng)險(xiǎn)，因?yàn)椋涝c加元是高度

45、相關(guān)的。為加元債務(wù)避險(xiǎn)的美元套期風(fēng)險(xiǎn)，因?yàn)椋涝c加元是高度相關(guān)的。為加元債務(wù)避險(xiǎn)的美元套期保值法：加元債務(wù)的現(xiàn)貨價(jià)格變化率與美元期貨價(jià)格變化率的關(guān)系如保值法：加元債務(wù)的現(xiàn)貨價(jià)格變化率與美元期貨價(jià)格變化率的關(guān)系如下：下： st/c$ = a a + b b futt/$+ et當(dāng)二者的期限匹配時(shí)，上式可變化為：當(dāng)二者的期限匹配時(shí)，上式可變化為：std/f1 = a a + b b std/f2 + etf1 = currency in which the underlying exposure is denominatedf2 = currency used to hedge against

46、the underlying exposure （由前面的公式轉(zhuǎn)化而來(lái)，由即期匯率變化率替代期貨匯率變化率是因（由前面的公式轉(zhuǎn)化而來(lái)，由即期匯率變化率替代期貨匯率變化率是因?yàn)槠谪浀狡跁r(shí)的價(jià)格與即期匯率具有趨同性。）為期貨到期時(shí)的價(jià)格與即期匯率具有趨同性。）-in this case, the currency of the underlying exposure (f1) is different from the currency of the futures contract (f2).-in the delta hedge, spot rate changes (std/f) were

47、regressed on changes in futures prices (futtd/f). -in the cross hedge, std/f2 is substituted for the independent variable futtd/f2 becausenthe maturity of the futures contract is the same as that of the underlying transaction in the spot market, andnfutures prices converge to spot prices at maturity.an example of a cme cross hedgenit is now january 18. you need to hedge a dkr （丹