第讲用于汇率风险管理的衍生产品货币期货与期货市场

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(违约动机）违约动机）eg,fx,$1.475/,当汇率上升时，卖方有违约动机，当汇率下降时，买方有违约动机。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（期货合约是一连串可更新的（期货合约是一连串可更新的1天期远期合约的组合：天期远期合约的组合： 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. 如三个月期的远期合约，相当于如三个月期的远期合约，相当于90个可更新的个可更新的1天期的远期合约天期的远期合约qdaily settlement is the biggest difference between a forward and a futures contractnfutures and forwards are nearly identical in their ability to hedge risk（在规避风险管理的功能上有相似之处）（在规避风险管理的功能上有相似之处）

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（即根据（即根据irp可以预测远期和期货价格）可以预测远期和期货价格）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（当存在（当存在期限错配时，基差风险使期货套期保值相对远期套期技术而期限错配时，基差风险使期货套期保值相对远期套期技术而言更有风险。）言更有风险。）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该公司利用期货合约套期该公司利用期货合约套期3月月13日日买进买进12月到期的期货合约，并月到期的期货合约，并在在10月月26日卖出该期货合约，风险在于日卖出

28、该期货合约，风险在于12月到期的期货合约运行到月到期的期货合约运行到10月月26日时的价格如何变化？即期货平仓时的价格是多少？日时的价格如何变化？即期货平仓时的价格是多少？n3月月13日，日，12月到期的期货合约价格：月到期的期货合约价格：fut0,t$/s$ = s0$/s$ (1+i$)/(1+is$)t (0.6010)(1+6.24%)/(1+4.04%)278/365=$0.6107/s$（以此价格买入）（以此价格买入）n同时，根据远期汇率预测法，同时，根据远期汇率预测法，10月月26日的即期汇率是：日的即期汇率是： 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日债务到期时，分三种情况讨论：日债务到期时，分三种情况讨论：情况一：基差不变：情况一：基差不变：basis i$-s$=6.24%-4.04%=2.20%,因此，因此，10月月26日的即期汇率不变，即日的即期汇率不变，即st$/s$ =$0.6

30、089/s$，在，在10月月26日，到日，到12月月16日交割的期货合约价格就建立在之前预期的即期汇率日交割的期货合约价格就建立在之前预期的即期汇率: st$/s$ =$0.6089/s$的基础上，期限的基础上，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=$0.6107/s$（ 以此价格卖出）以此价格卖出）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情况二：情况二：10月月26日，新加坡利率上升至：日，新加坡利率上升至： is$=4.54%，导致，导致新元汇率新元汇率上升至：上升至： st$/s$ =$0.6255/s$因此，在因此，在10月月26日，到日，到12月月16日交割的期货合约价格就变为：日交割的期货合约价格就变为： futt,t$/s$ = st$/s$ (1+i$)/(1+is$)t-t (0.6255)(1+6.24%)/(1+4.54

32、%)51/365=$0.6269/s$（以此价格卖出）（以此价格卖出）此时，公司在期货市场的收益为：此时，公司在期货市场的收益为：profit on futures: futt,t$/s$ - fut0,t$/s$ =$0.6269/s$0.6107/s$=$0.0162/s$新元升值带来的债务成本增加，即现货市场公司损失为：新元升值带来的债务成本增加，即现货市场公司损失为：loss on underlying short position in the spot currency: -(st$/s$ - est$/s$ )=-($0.6255/s$- $0.6089/s$=-$0.0166/

33、s$净损失净损失+0.01620.0166$0.0004/s$，损失总额为：，损失总额为：$4000（总（总债务支出是债务支出是10百万）百万）损失增加是因为新加坡利率上升，基差改变所致。损失增加是因为新加坡利率上升，基差改变所致。情况三：情况三：10月月26日，美元利率上升至：日，美元利率上升至： i$=6.74%，导致，导致新元汇率贬值至：新元汇率贬值至： st$/s$ =$0.5774/s$因此，在因此，在10月月26日，到日，到12月月16日交割的期货合约价格就变为：日交割的期货合约价格就变为： futt,t$/s$ = st$/s$ (1+i$)/(1+is$)t-t (0.5774

34、)(1+6.74%)/(1+4.04%)51/365=$0.5795/s$（以此价格卖出）（以此价格卖出）此时，公司在期货市场的损失为：此时，公司在期货市场的损失为：profit on futures: futt,t$/s$ - fut0,t$/s$ =$0.5795/s$-$0.6107/s$ =$0.0312/s$由于新元贬值，公司债务成本节约，即公司收益为：由于新元贬值，公司债务成本节约，即公司收益为：loss on underlying short position in the spot currency: -(st$/s$ - est$/s$ )=-($0.5774/s$- $0.

35、6089/s$=+$0.0315/s$净收益净收益 $0.0312/s$ +$0.0315/s$ +$0.0003/s$，收益总额为：，收益总额为：$3000所得增加是因为新加坡利率上升，基差改变所致。所得增加是因为新加坡利率上升，基差改变所致。但总的来讲，但总的来讲，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: 是指保值者持有期货合约的头寸规模与需要保值是指保值者持有期货合约的头寸规模与需要保值的基础资产之间的比率。的基础资产之间的比率。 the hedge ratio is used to minimize the variance of the hedged position.即期汇率变化率与期货汇率变化率的关系如下：即期汇率变化

37、率与期货汇率变化率的关系如下：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 （通过历史（通过历史数据对上式回归可以得出数据对上式回归可以得出b b ）nhedge quality （对冲质量）（对冲质量）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）之间）之间contract size mismatch and the hedge ratiocontract siz

40、e mismatch and the hedge ratio假设假设b b1.0251.025，则期货套期保值比率：，则期货套期保值比率： nfut*=(amount in futures)/(amount exposed) =-b b -1.025 -1.025 amount in futures （-1.025）（）（ amount exposed）如上例中，该公式有如上例中，该公式有10001000万新元的空头，需要持有的期货多头为万新元的空头，需要持有的期货多头为 amount in futures （-1.025）（ -10000000） s$10,250,000芝加哥商品期货交易所

41、一份新元期货合约金额为芝加哥商品期货交易所一份新元期货合约金额为125,000125,000，所以，所以，持有期货合约的规模为持有期货合约的规模为82 82 份期货合约份期货合约: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即选择的期货避险合约标的商品与现货商品不同，市场上没有类似现货即选择的期货避险合约标的商品与现货商品不同，市场上没有类似现货所发行的期货来避险时，就要找另一个现货价格有正相关，或者是同所发行的期货来避险时，就要找另一个现货价格有正相关，或者是同质的产品来避险。质的产品来避险。例如，一家英国公司有加元债务，可以利用美元期货的多头来规避汇率例如，一家英国公司有加元债务，可以利用美元期货的多头来规避汇率风险，因为，美元与加元是高度

45、相关的。为加元债务避险的美元套期风险，因为，美元与加元是高度相关的。为加元债务避险的美元套期保值法：加元债务的现货价格变化率与美元期货价格变化率的关系如保值法：加元债务的现货价格变化率与美元期货价格变化率的关系如下：下： st/c$ = a a + b b futt/$+ et当二者的期限匹配时，上式可变化为：当二者的期限匹配时，上式可变化为：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 （由前面的公式转化而来，由即期汇率变化率替代期货汇率变化率是因（由前面的公式转化而来，由即期汇率变化率替代期货汇率变化率是因为期货到期时的价格与即期汇率具有趋同性。）为期货到期时的价格与即期汇率具有趋同性。）-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