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1、 Chapter 2 Derivative Securities for Currency Risk Management Currency Futures and Futures Markets1用于汇率风险管理的衍生产品货币期货与期货市场 Chapter Overviewn1Financial Futures Exchangesn2The Operation of Futures Marketsn3Futures Contractsn4Forward versus Futures Market Hedgesn5Futures Hedges Using Cross Exchange Rate
2、sn6Hedging with Currency Futures2用于汇率风险管理的衍生产品货币期货与期货市场 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, fo
3、rward contracts. nThe last several sections discuss implementation issues:-Delta hedges for maturity mismatches-Cross hedges for currency mismatches-Delta-cross hedges for currency and maturity mismatches3用于汇率风险管理的衍生产品货币期货与期货市场 Forward Market1. Forward ContractsA forward contract is an agreement bet
4、ween a corporation and a commercial bank to exchange a specified amount 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
5、 rate at which they can purchase or sell a particular foreign currency. 4用于汇率风险管理的衍生产品货币期货与期货市场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
6、 $sThe forward contract provides a perfect hedge because the size and timing of the hedge transaction exactly offsets the size and timing of the underlying exposure. 5用于汇率风险管理的衍生产品货币期货与期货市场 Forward Market2. Non-Deliverable Forward Contractsa. New typenA non-deliverable forward contract (NDF) does no
7、t result in an actual exchange of currencies. Instead, one party makes a net payment to the other based on a market 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
8、on the exchange rate at the future date. 6用于汇率风险管理的衍生产品货币期货与期货市场nAn NDF can effectively hedge future foreign currency payments or receipts: 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)
9、= $.0020/peso.April 1Buy 100M Chilean pesos from market.July 1Index = $.0023/peso receive $30,000 from bank due to NDF. Index = $.0018/peso pay $20,000 to bank. 7用于汇率风险管理的衍生产品货币期货与期货市场 Forward versus Futures Contractsn Comparing currency futures contracts to currency forward contracts and shows how
10、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 incentive 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 ta
11、kes one side of every transaction (and makes sure that its exposures cancel one another)qContracts are marked-to-market daily qRequire initial and maintenance margins8用于汇率风险管理的衍生产品货币期货与期货市场 Forwards versus futuresForwardsFuturesCounterpartyBankCME Clearinghouse（Forward contracts are created by comme
12、rcial and investment banks, whereas futures contracts are usually found on futures exchanges）MaturityNegotiated3rd week of the month (US)AmountNegotiatedStandard contract sizeFeesBid-askCommissionsCollateralNegotiatedMargin accountSettlementAt maturityMost are settled early9用于汇率风险管理的衍生产品货币期货与期货市场Fut
13、ures exchangesnFinancial futures exchanges are usually associated with a commodity futures exchange2002 volumeTop 5 futures exchanges(million contracts)Eurex - Eurex (Germany & Switzerland)536.0CME - Chicago Mercantile Exchange (U.S.)444.5CBOT - Chicago Board of Trade (U.K.)276.3Euronext - (Amsterda
14、m, 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 10用于汇率风险管理的衍生产品货币期货与期货市场Forwards versus futuresnFutures contracts are similar to forward contractsqFutures contracts are lik
15、e 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 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
16、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）11用于汇率风险管理的衍生产品货币期货与期货市场 Hedging with futuresnForward contracts can be tailored
17、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 underlying exposures Currency mismatch - there may not be a fut
18、ures 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 not be an even increment of existing futures contracts 12
19、用于汇率风险管理的衍生产品货币期货与期货市场 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 through interest rate paritynIn
20、terest 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）Futt,Td/f = Ft,Td/f = Std/f (1+id
21、)/(1+if)T- -t STd/f (as t T)13用于汇率风险管理的衍生产品货币期货与期货市场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.14用于汇率风险管理的衍生产品货币期货与期货市场Maturity mismatches and basis risknIf there is a maturity mismatch, future
22、s contracts may not 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
23、of change in the relation 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。）15用于汇率风险管理的衍生产品货币期货与期货市场Maturity mismatche
24、s and Delta hedgesnFutures hedge is called 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.16用于汇率风险管理的衍生产品货币期货
25、与期货市场Dec 16Oct 26Mar 13-S$10millionunderlying obligationFutures expiration date following the cash flowAn example of a delta hedgetime 0time t=227/365Sept 11Futures expiration date following the cash flowtime T=278/36517用于汇率风险管理的衍生产品货币期货与期货市场An example of a delta hedgenThere are 227days between Marc
26、h 13 and October 26.nA hedge with the futures contract expires on September 11 only hedges against currency risk through that date. It remains exposed to changes in currency values from the end of the contract through October 26.nThe December futures contract is a better choice because it can hedge
27、currency risk through October 26 and then be sold.nSuppose the spot rate is S0$/s$0.6010/s$ 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
28、%)/(1+4.04%)227/365=$0.6089/s$nIt can form a perfect hedge with a long forward contract for delivery of S$10 million on October 26 in exchange for （$0.6089/s$)(S$10,000,000)=$6,089,000.As we shall see, the futures hedge using the December 16 futures contract is not quite as precise.18用于汇率风险管理的衍生产品货币
29、期货与期货市场An example of a delta hedgen该公司利用期货合约套期该公司利用期货合约套期3月月13日日买进买进12月到期的期货合约，并月到期的期货合约，并在在10月月26日卖出该期货合约，风险在于日卖出该期货合约，风险在于12月到期的期货合约运行到月到期的期货合约运行到10月月26日时的价格如何变化？即期货平仓时的价格是多少？日时的价格如何变化？即期货平仓时的价格是多少？n3月月13日，日，12月到期的期货合约价格：月到期的期货合约价格：Fut0,T$/s$ = S0$/s$ (1+i$)/(1+is$)T (0.6010)(1+6.24%)/(1+4.04%)278
30、/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$/s$ =$0.6089/s$This 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
31、三种情况讨论：日债务到期时，分三种情况讨论：19用于汇率风险管理的衍生产品货币期货与期货市场情况一：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$/S$ =$0.6089/s$，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
32、(0.6089)(1+6.24%)/(1+4.04%)51/365=$0.6107/s$（ 以此价格卖以此价格卖出）出）Profit on futures: Futt,T$/s$ - Fut0,T$/s$ =$0.6107/s$-$0.6107/s$=0Profit on underlying short position in the spot currency: -(St$/s$ - ESt$/s$ )=-(=$0.6089/s$- $0.6089/s$=020用于汇率风险管理的衍生产品货币期货与期货市场情况二：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$=4.
33、54%，导致，导致新元汇率新元汇率上升至：上升至： St$/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%)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$0.6107/s$=$0.0162/s
34、$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$/s$ )=-($0.6255/s$- $0.6089/s$=-$0.0166/s$净损失净损失+0.01620.0166$0.0004/s$，损失总额为：，损失总额为：$4000（总（总债务支出是债务支出是10百万）百万）损失增加是因为新加坡利率上升，基差改变所致。损失增加是因为新加坡利率上升，基差改变所致。21用于汇率风险管理的衍生产品货币期货与期货
35、市场情况三：情况三：10月月26日，美元利率上升至：日，美元利率上升至： i$=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)(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$/s$ -
36、 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$/s$ )=-($0.5774/s$- $0.6089/s$=+$0.0315/s$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
37、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. 22用于汇率风险管理的衍生产品货币期货与期货市场 Contract size mismatch and the Hedge RatioThe Forward Hedge: The hedge ratio NF*of a future position is defined as NF*=Amount in forward position/Amount
38、 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 ratefutt
39、d/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.The slope coefficient b b = r rs,fut (s ss / s sfut ) measures the sensitivity of spot to fu
40、tures prices23用于汇率风险管理的衍生产品货币期货与期货市场nfuttd/fstd/f24用于汇率风险管理的衍生产品货币期货与期货市场NFut*=(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-square (r2 = r rs,fut2). -r2 (or r rs,fut2) measures the percentage variation in std/f explai
41、ned 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 Ratio25用于汇率风险管理的衍生产品货币期货与期货市场Contract size 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
42、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$10,250,000芝加哥商品期货交易所一份新元期货合约金额为芝加哥商品期货交易所一份新元期货合约金额为125,000125,000，所以，所以，持有期货合约的规模为持有期
43、货合约的规模为82 82 份期货合约份期货合约:10,250,000/125,000=82:10,250,000/125,000=8226用于汇率风险管理的衍生产品货币期货与期货市场An example of a Hedge RationIt is now January 8. You need to hedge a 100 million obligation due on June 3. qThe spot exchange rate is S0$/ = $1.10/qA 100,000 CME euro futures contract expires on June 16qBased
44、on st$/ = a a + b b futt$/ + et , you estimate b b = 1.020 with r2 = 0.95.(The relatively high r2 (0.95) of this regression means that this is a relatively high quality hedge. )qHow many CME futures contracts should you buy to minimize the risk of your hedged position?27用于汇率风险管理的衍生产品货币期货与期货市场The Hed
45、ge Ratio solutionnThe optimal hedge ratio for this delta hedge is given byNFut* =(amount in futures)/(amount exposed) = -b(amount in futures) = (-b)(amount exposed) = (-1.020)(-100 million) = 102 millionor (102 million) / (100,000/contract) = 1,020 contracts28用于汇率风险管理的衍生产品货币期货与期货市场Currency mismatche
46、s and cross hedgesA cross hedge is used when there is a maturity match but a currency mismatch即选择的期货避险合约标的商品与现货商品不同，市场上没有类似现货即选择的期货避险合约标的商品与现货商品不同，市场上没有类似现货所发行的期货来避险时，就要找另一个现货价格有正相关，或者是同所发行的期货来避险时，就要找另一个现货价格有正相关，或者是同质的产品来避险。质的产品来避险。例如，一家英国公司有加元债务，可以利用美元期货的多头来规避汇率例如，一家英国公司有加元债务，可以利用美元期货的多头来规避汇率风险，因为，
47、美元与加元是高度相关的。为加元债务避险的美元套期风险，因为，美元与加元是高度相关的。为加元债务避险的美元套期保值法：加元债务的现货价格变化率与美元期货价格变化率的关系如保值法：加元债务的现货价格变化率与美元期货价格变化率的关系如下：下： st/c$ = 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
48、against 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。） 29用于汇率风险管理的衍生产品货币期货与期货市场-In this case, the currency of the underlying exposure (f1) is different from the currency of the futures contract (f2).-In the delta hedge
49、, spot rate changes (std/f) were 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 co
50、nverge to spot prices at maturity.30用于汇率风险管理的衍生产品货币期货与期货市场An example of a CME cross hedgenIt is now January 18. You need to hedge a DKr （丹麦（丹麦货币）货币）100 million obligation due on June 16. qSpot (cross) exchange rates are $0.75/DKr, 0.75/DKr, and $1.00/.qA CME futures contract expires on June 16 with
51、a contract size of 100,000nIn this cross hedge, there is a maturity match but a currency mismatch.qBased on st$/DKr = a a + b b st$/ + et , you estimate b b = 1.040 with r2 = 0.89. qHow many CME futures contracts should you buy to minimize the risk of your hedged position?31用于汇率风险管理的衍生产品货币期货与期货市场The
52、 cross hedge solutionOptimal hedge ratio:NFut* = (amt in futures)/(amt exposed) = -b (amt in futures) = (-b)(amt exposed) = (-1.040)(-DKr100 million) = DKr104 millionor 78 million at (DKr104m) (0.75/DKr) or 780 contracts. nWith an r-square of 0.89, this is a fairly high quality hedge. 32用于汇率风险管理的衍生产
53、品货币期货与期货市场 Delta-Cross Hedge （德尔塔交叉套期保值）（德尔塔交叉套期保值）n总结：总结：1.The most general case is the delta-cross hedge.nA delta-cross hedge is used when there is both a currency and a maturity mismatch std/f1 = a a + b b futtd/f2 + et2.If the underlying exposure and the futures contracts are in the same currenc
54、y, then f1 = f2 = f and the hedge is a delta hedge.3.If there is both a maturity and a currency match, then a futures hedge is nearly equivalent to a forward market hedge. std/f = a a + b b std/f + et由于由于std/f 与与std/f 的相关系数为的相关系数为+1，所以，是完全套期保值（，所以，是完全套期保值（r2=1），套期保值比率为），套期保值比率为NFut*=-b b1 1，此时期货套期保值
55、与远期套期保值是等值的，货币风险可以完全消除。，此时期货套期保值与远期套期保值是等值的，货币风险可以完全消除。4.A futures hedge is nearly perfect when there is a maturity and a currency match and the underlying transaction exposure is an even increment of the futures contract size. 33用于汇率风险管理的衍生产品货币期货与期货市场A classification of futures hedges34用于汇率风险管理的衍生产品货币期货与期货市场
