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1、 Chapter 3DerivativeSecuritiesforCurrencyRiskManagementCurrencyOptionsandOptionsMarkets圣经故事。在圣经故事。在圣经圣经创世记创世记第第2929章曾经提到过，大章曾经提到过，大约在公元前约在公元前17001700年，雅克布用七年的劳动购买了一个准许他年，雅克布用七年的劳动购买了一个准许他与拉班的女儿拉结结婚的期权。但是后来，拉班违约了，他与拉班的女儿拉结结婚的期权。但是后来，拉班违约了，他强迫雅克布与自己的大女儿利亚结了婚。雅克布照办了，但强迫雅克布与自己的大女儿利亚结了婚。雅克布照办了，但是，他深爱的仍然是
2、拉结。于是，他购买了另一个期权，即是，他深爱的仍然是拉结。于是，他购买了另一个期权，即再劳动七年以换得与拉结结婚。这一次，拉班没有食言。最再劳动七年以换得与拉结结婚。这一次，拉班没有食言。最后，雅克布娶了两个老婆，生了后，雅克布娶了两个老婆，生了1212个儿子。个儿子。圣经故事、橄榄压榨机与荷兰郁金香圣经故事、橄榄压榨机与荷兰郁金香 橄榄压榨机故事。古希腊的数学家和哲学家泰利斯在橄榄压榨机故事。古希腊的数学家和哲学家泰利斯在橄榄丰收之前利用期权获得了低价使用橄榄压榨机的权利。橄榄丰收之前利用期权获得了低价使用橄榄压榨机的权利。据说，他是第一个利用期权交易致富的人。泰利斯生活在公元据说，他是第一
3、个利用期权交易致富的人。泰利斯生活在公元前前580580年左右古希腊的米利塔斯市，位于今天土耳其的西南海岸。年左右古希腊的米利塔斯市，位于今天土耳其的西南海岸。泰利斯运用自己的天文知识在冬季就预测到橄榄在来年春天将泰利斯运用自己的天文知识在冬季就预测到橄榄在来年春天将获得丰收。虽然没有什么钱，然而他用自己所有的积蓄在冬季获得丰收。虽然没有什么钱，然而他用自己所有的积蓄在冬季淡季就以低价取得了春季旺季所有压榨机的使用权。淡季就以低价取得了春季旺季所有压榨机的使用权。当然，他支付的价格也很低，因为当时没有人认为有必要为了当然，他支付的价格也很低，因为当时没有人认为有必要为了这些压榨机来竞价。当春天
4、橄榄获得大丰收时，每个人都想找这些压榨机来竞价。当春天橄榄获得大丰收时，每个人都想找到压榨机。这时，泰利斯执行他的权利，将压榨机以高价出租，到压榨机。这时，泰利斯执行他的权利，将压榨机以高价出租，结果赚了一大笔钱。结果赚了一大笔钱。圣经故事、橄榄压榨机与荷兰郁金香圣经故事、橄榄压榨机与荷兰郁金香 荷兰郁金香故事。在荷兰郁金香故事。在1717世纪世纪3030年代的年代的“荷兰郁金香热荷兰郁金香热”时期，郁金香的一些品种堪称欧洲最为昂贵的稀世花卉。时期，郁金香的一些品种堪称欧洲最为昂贵的稀世花卉。16351635年，那些珍贵品种的郁金香球茎供不应求，加上投机炒作，年，那些珍贵品种的郁金香球茎供不应
5、求，加上投机炒作，致使价格飞涨致使价格飞涨2020倍，成为最早有记载的泡沫经济。倍，成为最早有记载的泡沫经济。这股投机狂潮却开启了期权交易的大门。郁金香交易商向种植者这股投机狂潮却开启了期权交易的大门。郁金香交易商向种植者收取一笔费用，授予种植者按约定最高价格向该交易商出售郁金收取一笔费用，授予种植者按约定最高价格向该交易商出售郁金香球茎的权利（卖权）。香球茎的权利（卖权）。同时，郁金香交易商通过支付给种植者一定数额的费用，以获取同时，郁金香交易商通过支付给种植者一定数额的费用，以获取以约定的最低价格购买球茎的权利（买权）。以约定的最低价格购买球茎的权利（买权）。这种交易对于降低郁金香交易商和
6、种植者的风险十分有用。这种交易对于降低郁金香交易商和种植者的风险十分有用。圣经故事、橄榄压榨机与荷兰郁金香圣经故事、橄榄压榨机与荷兰郁金香 Chapter OverviewnWhat is an optionnOption payoff profilesnCombinations of optionsnThe determinants of currency option valuesnHedging with currency options A forward obligationSupposeaU.S.companyhasaforwardobligationof1milliondueat
7、timeTinfourmonths.CurrentspotandforwardratesareS0$/=FT$/=$1.45/.nTheexpectedamountdueonthisforwardobligationisECFT$=(ECFT)(EST$/)=(1,000,000)($1.45/)=$1,450,000.nIftheactualexchangerateis$1.50/,thenthis1millionobligationwillcostCFT$=(CFT)(ST$/)=(1,000,000)($1.50/)=$1,500,000.qInthiscase,theU.S.compa
8、nyhasanunexpectedlossof$50,000. Underlying transaction-1,000,000Currency exposureDV$/DS$/ A forward hedgenThisforwardexposurecanbehedgedbybuyingpoundsterlingintheforwardmarket,whichinthiscasemeanssimultaneouslysellingdollarsforward.nBuy1millionintheforwardmarketattheforwardpriceF1$/=$1.45/nThecashfl
9、owtimelineandthepayoffprofileoftheforwardcontractareshownontheslidebasedontheforwardrateofexchangeisFT$/=$1.45/.IftheactualexchangerateisST$/=$1.50/,thenpurchasing1,000,000attheforwardpriceofFT$/=$1.45/willsaveyou$50,000andoffsetyourlossontheunderlyingexposure.Conversely,ifthepoundfallsto$1.40/,youw
10、illgain$50,000ontheunderlyingobligationbutlose$50,000ontheforwardcontract.A forward hedgenWouldnt it be nice to own an insurance policy against a rise in the exchange rate without a corresponding loss if exchange rates fall?Long pound forward+1,000,000-$1,450,000Exposure of forward contractDV$/DS$/A
11、n option hedgenAcurrencyoptionislikeone-halfofaforwardcontractqtheoptionholdergainsifpoundsterlingrisesqtheoptionholderdoesnotloseifpoundsterlingfallsLongpoundcall(option to buypound sterling)DS$/DV$/An option hedgenOptionsareusedfortwopurposes:-Hedging-SpeculationHedgingisbyfarthemorecommonusebycor
12、poratefinancialmanagers.nInthisexample,acalloptiononpoundsterlingactsasaninsurancepolicy(ahedge)againstariseinthevalueofthepound.-IftheactualexchangeraterisestoST$/=$1.50/atexpiration,thentheoptionprovidesapayoffof(1,000,000)($0.05/)=$50,000.-IftheactualexchangeratefallstoST$/=$1.40/,thentheoptionis
13、out-of-the-moneyandisnotexercised.nOfcourse,thisinsurancepolicydoesnotcomefree.Thecostoftheoptioniscalledtheoptionpremium.Theoptionholderpaystheoptionpremiumwhentheoptionispurchased.Options Contracts: PreliminariesnA foreign currency option is a contract giving the option purchaser (the buyer) the r
14、ight, but not the obligation, to buy or sell a given amount of foreign exchange at a fixed price per unit for a specified time period (until the maturity date).nThe buyer of an option is termed the holder, while the seller of the option is referred to as the writer or grantor.nEvery option has three
15、 different price elements:qThe exercise or strike price the exchange rate at which the foreign currency can be purchased (call) or sold (put)qThe premium the cost, price, or value of the option itselfqThe underlying or actual spot exchange rate in the marketOptions Contracts: PreliminariesnAnoptiong
16、ivestheholdertheright,but not the obligation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.nCallsvs.PutsqCalloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.qPutoptionsgivestheholdertheright,butnott
17、heobligation,tosellagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.Options Contracts: PreliminariesnEuropeanvs.AmericanoptionsqEuropeanoptionscanonlybeexercisedontheexpirationdate.qAmericanoptionscanbeexercisedatanytimeuptoandincludingtheexpirationdate.qSincethisoptiontoexerci
18、seearlygenerallyhasvalue,AmericanoptionsareusuallyworthmorethanEuropeanoptions,otherthingsequal.Options Contracts: PreliminariesnIntrinsic ValueqThe difference between the exercise price of the option and the spot price of the underlying asset.nSpeculative ValueqThe difference between the option pre
19、mium and the intrinsic value of the option.Option Premium=Intrinsic ValueSpeculative Value+Currency Options MarketsnPHLX(费城证券交易所费城证券交易所)nHKFE（香港期货交易所）（香港期货交易所）n20-hourtradingday.nOptions on the over-the-counter (OTC) market can be tailored to the specific needs of the firm but can expose the firm to
20、 counterparty risk.nOptions on organized exchanges are standardized, but counterparty risk is substantially reduced.nOTCvolumeismuchbiggerthanexchangevolume.nTradingisinsevenmajorcurrenciesplustheeuroagainsttheU.S.dollar.PHLX Currency Option SpecificationsCurrencyContractSizeAustralian dollarAD50,00
21、0British pound31,250Canadian dollarCD50,000Euro62,500Japanese yen6,250,000Swiss francSF62,500Foreign Currency OptionsStatus of an optiona.In-the-moneyCall: Spot strikePut:Spot strikeb.Out-of-the-moneyCall: Spot strikec.At-the-moneySpot = the strike Currency Futures OptionsnAre an option on a currenc
22、y futures contract.nExercise of a currency futures option results in a long futures position for the holder of a call or the writer of a put.nExercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put.nFirms may purchase currency call opt
23、ions to nThey may purchase currency call optionsqto hedge future payables;qto hedge potential expenses when bidding on projects; andqto hedge potential costs when attempting to acquire other firms.nSpeculators may purchase call options on a currency that they expect to appreciate. Profit =selling (s
24、pot) price option premium buying (strike) pricenThey may also sell (write) call options on a currency that they expect to depreciate.qProfit = option premium buying (spot) price+ selling (strike) price The functions of Call OptionnThe purchaser of a call option will break even when selling price =bu
25、ying (strike) price + option premiumnThe seller (writer) of a call option will break even whenn buying price = selling (strike) price+ option premiumBreakeven on Call OptionESTProfitlossc0E + c0Long callESTProfitlossc0E + c0short 1 callnFirms may purchase currency put options to hedge future receiva
26、bles.nSpeculators may purchase put options on a currency that they expect to depreciate. qProfit =selling (strike) price buying price option premiumnThey may also sell (write) put options on a currency that they expect to appreciate. nProfit = option premium + selling price buying (strike) priceThe
27、functions of Put OptionESTProfitloss p0E p0long putE p0ESTProfit p0E p0short put E + p0BreakevenonPutOptionThepurchaserofaputoptionwillbreakevenwhenbuyprice=selling(strike)price-optionpremiumTheseller(writer)ofaputoptionwillbreakevenwhen sellingprice=buying(strike)price-optionpremiumPayoff profile o
28、f a call option at expirationLongcallShortcallST$/CallT$/KT$/ST$/-CallT$/KT$/In-the-moneyOut-of-the-moneyOut-of-the-moneyIn-the-moneyCurrency options are a zero-sum game; gains on one side are offset by losses on the other.Payoff profile of a put option at expirationShortputKT$/LongputST$/PutT$/ST$/
29、-PutT$/KT$/In-the-moneyOut-of-the-moneyOut-of-the-moneyIn-the-moneyAs in the previous slide, options are a zero-sum game; gains on one side are offset by losses on the other. Forwards, puts, and callsA Forward by Any Other NamenA combination of a longcall and a shortput at the same exercise price an
30、d with the same expiration date results in a longforward position at that forward priceDST$/DCallT$/DFT$/-DPutT$/DST$/DST$/LongcallShortputLongforward+= Forwards, puts, and calls A Forward by Any Other NameConversely, a short call and a long put with the same exercise price and expiration date is eq
31、uivalent to a short forward position.DST$/-DCallT$/-DFT$/DPutT$/DST$/DST$/ShortcallLongputShortforward+=A Forward by Any Other Name : Put-call parityLongforward=FT$/ST$/-PutT$/ST$/Shortput+ST$/CallT$/LongcallKT$/ST$/+ExercisepriceKT$/Put-call parity relates call and put values to the value of a forw
32、ard contract.nWhen we want to talk about the value (rather than changes in the value) of a long call and a short put, we need to adjust for the exercise price.The general case is called “put-call parity” and relates the value of a long call, a short put, the exercise price, and the forward price at
33、expiration:CallTd/f - PutTd/f + Kd/f = FTd/f Combinations of options -A Straddle optionnOne possible speculative strategy for volatile currencies is to purchase both a put option and a call option at the same exercise price. This is called a straddle. nLong straddle=a long call and a long put on the
34、 same underlying asset and with the same exercise price. nShort straddle=a short call and a short put on the same underlying asset and with the same exercise price. KTSTSTKTVTVTLong straddleShort straddle Combinations of options -A Straddle optionnHeresanexample,Inearly1995,aroguetradernamedNickLess
35、ondrovedtheUnitedKingdomsBaringsBankintobankruptcythroughunauthorizedspeculationinNikkeistockindexfuturesontheSingaporeandOsakastockexchanges.nLeesonsoldoptionstraddlesontheNikkeiindexatatimewhenvolatilityontheindexwaslow.nLeesonformedashortstraddlebysimultaneouslysellingcallsandputontheNikkeiindex.
36、nIncludingtheproceedsfromthesaleofthecallandtheput,theprofit/lossdiagramontheshortstraddlepositionatexpirationlookslikethis:profit/loss on a short straddleSTNikkeiKTNikkeiVTNikkeiHe placed a bet on the volatility of the Nikkei index. As long as the Nikkei index did not vary too much, Leeson would ha
37、ve won his bet.Leeson loses if the Nikkei index rises too high or falls too low.The fact was: Volatility on the Nikkei index was low at the time Leeson sold his position. As it turned out, the Nikkei index fell below the profitable range.LeesonincurredfurtherlossesbybuyingfuturesontheNikkeiindexinth
38、ehopesofarecoverythat,toBaringsregret,neveroccurred. The Determinants of Option ValuesAmericancurrencyoptionspriortoexpirationpricedaccordingtotheBlack-Scholesmodelare:OptionvaluedeterminantCalld/fPutd/f1.Underlyingexchangerate(Sd/f)+- -2.Exerciseprice(Kd/f)- -+3.Risklessrateincurrencyd(id)+- -4.Ris
39、klessrateincurrencyf (if)- -+5.Timetoexpiration(T)+6.Exchangeratevolatility (sd/f)+nOption value = Time value + intrinsic valueIntrinsic Value, Time Value & Total Value for a Call Option on British Pounds with a Strike Price of $1.70/n 1.691.701.711.721.731.681.671.660.01.02.03.04.05.0Spot rate ($/)
40、Option Premium(US cents/)3.305.674.006.01.741.67Total valueIntrinsic valueTime value- Valuation on first day of 90-day maturity - IntrinsicValue,TimeValue&TotalValueforaCallOptiononBritishPoundswithaStrikePriceof$1.70/The Intrinsic Value of an OptionnTheintrinsicvalueofanoptionisthevalueoftheoptioni
41、fitisexercisedtoday.nCalloptionvaluewhenexercised=Max(std/f-kd/f),0nPutoptionvaluewhenexercised=Max(kd/f-std/f),0nifacallorputoptionisout-of-money,itsintrinsicvalueiszero.Ifanoptionisin-the-money,itsintrinsicvalueisequaltothedifferencebetweentheexercisepriceandthevalueoftheunderlyingasset. Ex: For S
42、ept 1.60 put option on BritishPound, spot rate is $1.5841, theoption premium is $0.0220, computeintrinsic value and time value. Intrinsic value=X - S =1.60 - 1.5841 = $0.0159Time value= P - intrinsic value =0.0220-0.0159= $0.0061 The time value of an optionnTime value = Option value - intrinsic valu
43、eqIntrinsicvalue = value if exercised immediatelynThe timevalue of a currency option is a function of the following six determinantsqExchangerateunderlying the optionqExercisepriceor striking price qRisklessrateof interest id in currency dqRisklessrate of interest if in currency fqVolatility in the
44、underlying exchange rateqTimetoexpirationThetwomostcriticalvariablesarevolatilityintheunderlyingexchangerateandthetimetoexpiration.The time value of an optionnTime value = Option value - intrinsic valueAsexchangeratevolatilityincreases,thevaluesofAmericancallandputoptionsincrease.Asthetimetoexpirati
45、onincreases,thevaluesofAmericancallandputoptionsincrease.Thatis,Americanoptionvaluesaregreaterifvolatilityintheunderlyingassetincreasesorifthetimetoexpirationislonger.Becauseoptionholderscontinuetogainononesideoftheexercisepricebutdonotsuffercontinuedlossesontheotherside,optionsbecomemorevaluableast
46、heend-of-periodexchangeratedistributionbecomesmoredispersed.The time value of an optionnAsexpiration,onlythatportionoftheexchangeratedistributionthatexpiresin-the-moneyhasvalue.nTheout-of-themoneycalloptionhaslittlevaluebecausethereislittlelikelihoodofthespotrateclimbingabovetheexerciseprice.nAsthev
47、ariabilityofend-of-periodexchangeratesincreases,thereisanincreasingprobabilitythatthespotratewillcloseabovetheexerciseprice.nAsthemoreout-of-themoneytheoptionis,thetimevalueissmaller.n价外期权越大，时间价值越小价外期权越大，时间价值越小由于价外期权行使的机会很低，立权人选择不进行套期保值。这种策略的风由于价外期权行使的机会很低，立权人选择不进行套期保值。这种策略的风险是对应资产的价格可能狂升，使该期权到期时变成价
48、内。如果这样，立险是对应资产的价格可能狂升，使该期权到期时变成价内。如果这样，立权人被迫在市场上以比当期高得多的价格购买对应资产，从而遭受损失。权人被迫在市场上以比当期高得多的价格购买对应资产，从而遭受损失。但是，期权订立时的价外越大，对应资产价格上升到价内的可能性越小，立但是，期权订立时的价外越大，对应资产价格上升到价内的可能性越小，立权人风险就越低，因此其时间价值就越低。权人风险就越低，因此其时间价值就越低。Exchange rate volatility and out-of-the-money call option value CallTd/fSTd/fSTd/f CallTd/fS
49、Td/fSTd/f The time value of an optionnAnat-the-moneycalloptiongainsifthespotrateclosesfartherabove,theexercisepricebutdoesnotloseifthespotrateclosesfartherbelostheexerciseprice.nAsthevariabilityofend-of-periodexchangeratesincreases,anareaofthedistributionfallsfartherin-the-moneyandtheoptionsismoreva
50、luable.n平价期权的时间价值最大平价期权的时间价值最大由于到期时平价期权被执行的概率为由于到期时平价期权被执行的概率为50%。那么期权立权人是否要购买对应。那么期权立权人是否要购买对应资产进行套期保值呢？如果已经购买了，而期权到期时为价外，则遭受损资产进行套期保值呢？如果已经购买了，而期权到期时为价外，则遭受损失。如果不购买，而期权到期时为价内，再从市场上购买对应资产也要遭失。如果不购买，而期权到期时为价内，再从市场上购买对应资产也要遭受损失。因此，受损失。因此，订立平价期权使立权人面临最大的不确定性。因此，此时订立平价期权使立权人面临最大的不确定性。因此，此时时间价值最大。时间价值最大
51、。Exchange rate volatility and at-the-money call option value CallTd/fSTd/fSTd/f CallTd/fSTd/fSTd/fThe time value of an optionnForin-the-moneycalloption,ifanunderlyingexchangerateisbelowtheexercisepriceatexpiration,theoptionhaszerovalueregardlessofthehowfartheclosingpricefallsbelowtheexerciseprice.nO
52、ntheotherhand,asthespotrateincreases,thecalloptioncontinuestoincreaseinvalue.nThus,in-the-moneycalloptionsbenefitfromhighervolatility.n价内期权越多，时间价值越小价内期权越多，时间价值越小在这种情况下，期权很可能被行使，因此，在这种情况下，期权很可能被行使，因此，立权人需要买入对应资产进立权人需要买入对应资产进行套期行套期。这种策略有一种风险，对应资产的价格下降很快，期权到期。这种策略有一种风险，对应资产的价格下降很快，期权到期时为价外，立权人就无法卖出对应资产
53、（因为期权不被行使）。此时，时为价外，立权人就无法卖出对应资产（因为期权不被行使）。此时，在市场上卖出对应资产将遭受损失。在市场上卖出对应资产将遭受损失。但是，但是，期权在订立时价内越多，这种风险发生的机会就越小，因此，当期权在订立时价内越多，这种风险发生的机会就越小，因此，当期权价内越多时，时间价值越小。期权价内越多时，时间价值越小。Exchange rate volatility and in-the-money call option value CallTd/fSTd/fSTd/f CallTd/fSTd/fSTd/fIntrinsic Value, Time Value & Tota
54、l Value for a Call Option on British Pounds with a Strike Price of $1.70/n 上表表示：在到期日前，只要还有时间存在，期权就有时上表表示：在到期日前，只要还有时间存在，期权就有时间价值。正是这一特征，使得美式期权的持有者很少有到间价值。正是这一特征，使得美式期权的持有者很少有到期日前行使其期权，持有者可以将其手中持有的期权转卖期日前行使其期权，持有者可以将其手中持有的期权转卖而不会行使。而不会行使。 货币期权定价的敏感性分析货币期权定价的敏感性分析n1.对即期汇率变化的敏感性（对即期汇率变化的敏感性（Delta）:Opti
55、onsdeltaisalsocalledthehedgeratio:thechangeinoptionpricewithrespecttoachangeinspotrate.（期权价格对即期汇率（期权价格对即期汇率变化的敏感性称为变化的敏感性称为Delta值）值）Ex: =20%,S=$0.72,C0=$0.0395.Ifspotratechangesto$0.71,C1=$0.0335,findtheDelta.nDelta= C/ S=(0.0395-0.0335)/(0.72-0.71)=$0.6该结果表明：如果给定该结果表明：如果给定Delta值值0.6，那么，即期汇率变化，那么，即期
56、汇率变化1美分美分（$0.01/）,期权费变化将是期权费变化将是0.60.010.006$。如果初始期。如果初始期权费是是$0.0395/,即期即期汇率减少率减少1美分（从美分（从$1.72/减少到减少到$1.71/），），则新的期新的期权费就就应该为$0.0395-$0.006=$0.0335/一般地，看一般地，看涨期期权的的Delta值变化在值变化在+1和和0之间。而看跌期权的之间。而看跌期权的Delta值变值变化在化在1和和0之间之间交易者根据Delta 值对期权分类值对期权分类nThehigherthedelta,thegreatertheprobabilityoftheoptione
57、xpiringin-the-money。n当期权朝实值期权变化时，当期权朝实值期权变化时，Delta值就上升趋向于值就上升趋向于1.0；n当期权朝虚值期权变化时，当期权朝虚值期权变化时，Delta值就下降趋向于值就下降趋向于0；看涨期权费的分解看涨期权费的分解协定价协定价格格（$/）即期价即期价格格看涨期权费看涨期权费内在价值内在价值时间价值时间价值（美分（美分/）（）（美分美分/）+（美分（美分/）Delta值值1.701.701.701.751.701.656.375.001.373.300.003.301.370.001.370.710.500.282.离到期日的离到期日的时间（thet
58、a）期期权的价的价值随离到期日的随离到期日的时间长度而增加，度而增加，预期期期期权费的的变化与到期化与到期日日时间变化的比化的比值称称为Optionstheta：thechangeinoptionpricewithrespecttoaChangeinmaturity.Ex: =20%,S=$0.72,T=20days,C0=$0.0288.IfT=18days,C1=$0.0241,computethetheta.theta=(0.0241-0.0288)/(18-20)=0.00235值得注意的是，得注意的是，theta值与时间的关系不是线性关系，而是时间的平值与时间的关系不是线性关系，而是
59、时间的平方根。例如，方根。例如，3个月和个月和1个月的实值期权的期权费关系是：个月的实值期权的期权费关系是：即即3月期的期权费只是月期的期权费只是1月期期权费的月期期权费的1.73倍，倍，而不是而不是3倍。离到期日越近，期权价值衰减越厉害！倍。离到期日越近，期权价值衰减越厉害！ 货币期权定价的敏感性分析货币期权定价的敏感性分析时间价值的衰减对期权交易者来说非时间价值的衰减对期权交易者来说非常重要。常重要。n交易者购买一个交易者购买一个1月期或月期或2月期到期的期权，其期权的月期到期的期权，其期权的价值迅速衰减。价值迅速衰减。n同样地，他购买一个同样地，他购买一个6月期的期权费比月期的期权费比1
60、月期的期权费月期的期权费贵贵2.45倍，而倍，而12月期的期权费仅比月期的期权费仅比1月期的期权费贵月期的期权费贵3.46倍。倍。n所以，所以，交易者通常发现较长到期日的期权有较好的价交易者通常发现较长到期日的期权有较好的价值！值！Days remaining to maturityOption Premium(US cents/)A Call Option on British Pounds: Spot Rate = $1.70/0.01.02.03.04.05.06.07.09080706050403020100In-the-money (ITM) call ($1.65 strike p
61、rice)At-the-money (ATM) call ($1.70 strike price)Out-of-the-money (OTM) call ($1.75 strike price)Theta: Option Premium Time Value Deterioration3.对波波动率的敏感性（率的敏感性（Lambda）期期权的波的波动率定率定义为基基础汇率每日百分比率每日百分比变化的化的标准差。准差。波波动率率对期期权价价值的重要性是因的重要性是因为如果如果汇率的波率的波动率增加，期率增加，期权被行使的被行使的风险增加，期增加，期权费可能上升。可能上升。如，期如，期权的年波的年
62、波动率率为12.6%，则每日的波每日的波动率的百分比率的百分比为：OptionsLambda：期：期权费对波波动率率1个个单位位变化的敏感性用化的敏感性用表示表示Ex: =10%,S=$0.72,C0=$0.0266Ifvolatility( )risesto20%,C1=$0.0395Lambda=(0.0395-0.0266)/(0.2-0.1)=0.129 货币期权定价的敏感性分析货币期权定价的敏感性分析Lambda: Option Premium Sensitivity to Volatility when the Spot Rate is $1.70/n 4.对利率利率变化差异的敏感
63、性（化差异的敏感性（OptionsRhoandPhi）从期从期权费的构成看出：期的构成看出：期权费与利率呈正相关。由于国内与利率呈正相关。由于国内利率与国外利率水平会影响到利率与国外利率水平会影响到汇率，因此，我率，因此，我们定定义：国内利率水平的微小国内利率水平的微小变化化对期期权费的影响称的影响称为Rho；而国外利率水平的微小变化对期权费的影响称为而国外利率水平的微小变化对期权费的影响称为PhiRho= C/ rdRhi= C/ rfEx:T=91, =20%,S=$0.72,rd=4.76%,C0=$0.0395.Ifdomesticinterestrateincreasesto5%,C1=$0.0392,computetheRho.Rho=(0.0392-0.0395)/(0.05-0.0476)=-0.125 货币期权定价的敏感性分析货币期权定价的敏感性分析Interest Differentials and Call Option Premiums when the Spot Rate is $1.70/n Summary of Option Premium ComponentsnSummary of Option Premium Components
