用于汇率风险管理的衍生产品：货币期权与期权市场

Chapter3,DerivativeSecuritiesforCurrencyRiskManagementCurrencyOptionsandOptionsMarkets,圣经故事。在圣经创世记第29章曾经提到过，大约在公元前1700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。最后，雅克布娶了两个老婆，生了12个儿子。,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。泰利斯生活在公元前580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。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，结果赚了一大笔钱。,圣经故事、橄榄压榨机与荷兰郁金香,荷兰郁金香故事。在17世纪30年代的“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。1635年，那些珍贵品种的郁金香球茎供不应求，加上投机炒作，致使价格飞涨20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）。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）。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,ChapterOverview,WhatisanoptionOptionpayoffprofilesCombinationsofoptionsThedeterminantsofcurrencyoptionvaluesHedgingwithcurrencyoptions,Aforwardobligation,SupposeaU.S.companyhasaforwardobligationof1milliondueattimeTinfourmonths.CurrentspotandforwardratesareS0$/=FT$/=$1.45/.TheexpectedamountdueonthisforwardobligationisECFT$=(ECFT)(EST$/)=(1,000,000)($1.45/)=$1,450,000.Iftheactualexchangerateis$1.50/,thenthis1millionobligationwillcostCFT$=(CFT)(ST$/)=(1,000,000)($1.50/)=$1,500,000.Inthiscase,theU.S.companyhasanunexpectedlossof$50,000.,Aforwardhedge,Thisforwardexposurecanbehedgedbybuyingpoundsterlingintheforwardmarket,whichinthiscasemeanssimultaneouslysellingdollarsforward.Buy1millionintheforwardmarketattheforwardpriceF1$/=$1.45/ThecashflowtimelineandthepayoffprofileoftheforwardcontractareshownontheslidebasedontheforwardrateofexchangeisFT$/=$1.45/.IftheactualexchangerateisST$/=$1.50/,thenpurchasing1,000,000attheforwardpriceofFT$/=$1.45/willsaveyou$50,000andoffsetyourlossontheunderlyingexposure.Conversely,ifthepoundfallsto$1.40/,youwillgain$50,000ontheunderlyingobligationbutlose$50,000ontheforwardcontract.,Aforwardhedge,Wouldntitbenicetoownaninsurancepolicyagainstariseintheexchangeratewithoutacorrespondinglossifexchangeratesfall?,Anoptionhedge,Acurrencyoptionislikeone-halfofaforwardcontracttheoptionholdergainsifpoundsterlingrisestheoptionholderdoesnotloseifpoundsterlingfalls,Longpoundcall(optiontobuypoundsterling),Anoptionhedge,Optionsareusedfortwopurposes:HedgingSpeculationHedgingisbyfarthemorecommonusebycorporatefinancialmanagers.Inthisexample,acalloptiononpoundsterlingactsasaninsurancepolicy(ahedge)againstariseinthevalueofthepound.IftheactualexchangeraterisestoST$/=$1.50/atexpiration,thentheoptionprovidesapayoffof(1,000,000)($0.05/)=$50,000.IftheactualexchangeratefallstoST$/=$1.40/,thentheoptionisout-of-the-moneyandisnotexercised.Ofcourse,thisinsurancepolicydoesnotcomefree.Thecostoftheoptioniscalledtheoptionpremium.Theoptionholderpaystheoptionpremiumwhentheoptionispurchased.,OptionsContracts:Preliminaries,Aforeigncurrencyoptionisacontractgivingtheoptionpurchaser(thebuyer)theright,butnottheobligation,tobuyorsellagivenamountofforeignexchangeatafixedpriceperunitforaspecifiedtimeperiod(untilthematuritydate).Thebuyerofanoptionistermedtheholder,whiletheselleroftheoptionisreferredtoasthewriterorgrantor.Everyoptionhasthreedifferentpriceelements:Theexerciseorstrikepricetheexchangerateatwhichtheforeigncurrencycanbepurchased(call)orsold(put)Thepremiumthecost,price,orvalueoftheoptionitselfTheunderlyingoractualspotexchangerateinthemarket,OptionsContracts:Preliminaries,Anoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.Callsvs.PutsCalloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.,OptionsContracts:Preliminaries,Europeanvs.AmericanoptionsEuropeanoptionscanonlybeexercisedontheexpirationdate.Americanoptionscanbeexercisedatanytimeuptoandincludingtheexpirationdate.Sincethisoptiontoexerciseearlygenerallyhasvalue,AmericanoptionsareusuallyworthmorethanEuropeanoptions,otherthingsequal.,OptionsContracts:Preliminaries,IntrinsicValueThedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.SpeculativeValueThedifferencebetweentheoptionpremiumandtheintrinsicvalueoftheoption.,OptionPremium,=,IntrinsicValue,SpeculativeValue,+,CurrencyOptionsMarkets,PHLX(费城证券交易所)HKFE（香港期货交易所）20-hourtradingday.Optionsontheover-the-counter(OTC)marketcanbetailoredtothespecificneedsofthefirmbutcanexposethefirmtocounterpartyrisk.Optionsonorganizedexchangesarestandardized,butcounterpartyriskissubstantiallyreduced.OTCvolumeismuchbiggerthanexchangevolume.TradingisinsevenmajorcurrenciesplustheeuroagainsttheU.S.dollar.,PHLXCurrencyOptionSpecifications,ForeignCurrencyOptions,Statusofanoptiona.In-the-moneyCall:SpotstrikePut:Spotstrikec.At-the-moneySpot=thestrike,CurrencyFuturesOptions,Areanoptiononacurrencyfuturescontract.Exerciseofacurrencyfuturesoptionresultsinalongfuturespositionfortheholderofacallorthewriterofaput.Exerciseofacurrencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput.,FirmsmaypurchasecurrencycalloptionstoTheymaypurchasecurrencycalloptionstohedgefuturepayables;tohedgepotentialexpenseswhenbiddingonprojects;andtohedgepotentialcostswhenattemptingtoacquireotherfirms.Speculatorsmaypurchasecalloptionsonacurrencythattheyexpecttoappreciate.Profit=selling(spot)priceoptionpremiumbuying(strike)priceTheymayalsosell(write)calloptionsonacurrencythattheyexpecttodepreciate.Profit=optionpremiumbuying(spot)price+selling(strike)price,ThefunctionsofCallOption,Thepurchaserofacalloptionwillbreakevenwhensellingprice=buying(strike)price+optionpremiumTheseller(writer)ofacalloptionwillbreakevenwhenbuyingprice=selling(strike)price+optionpremium,BreakevenonCallOption,Firmsmaypurchasecurrencyputoptionstohedgefuturereceivables.Speculatorsmaypurchaseputoptionsonacurrencythattheyexpecttodepreciate.Profit=selling(strike)pricebuyingpriceoptionpremiumTheymayalsosell(write)putoptionsonacurrencythattheyexpecttoappreciate.Profit=optionpremium+sellingpricebuying(strike)price,ThefunctionsofPutOption,BreakevenonPutOption,Thepurchaserofaputoptionwillbreakevenwhenbuyprice=selling(strike)price-optionpremiumTheseller(writer)ofaputoptionwillbreakevenwhensellingprice=buying(strike)price-optionpremium,Payoffprofileofacalloptionatexpiration,Longcall,Shortcall,In-the-money,Out-of-the-money,Out-of-the-money,In-the-money,Currencyoptionsareazero-sumgame;gainsononesideareoffsetbylossesontheother.,Payoffprofileofaputoptionatexpiration,Shortput,KT$/,In-the-money,Out-of-the-money,Out-of-the-money,In-the-money,Asinthepreviousslide,optionsareazero-sumgame;gainsononesideareoffsetbylossesontheother.,Forwards,puts,andcallsAForwardbyAnyOtherName,Acombinationofalongcallandashortputatthesameexercisepriceandwiththesameexpirationdateresultsinalongforwardpositionatthatforwardprice,Forwards,puts,andcallsAForwardbyAnyOtherName,Conversely,ashortcallandalongputwiththesameexercisepriceandexpirationdateisequivalenttoashortforwardposition.,AForwardbyAnyOtherName:Put-callparity,KT$/,ST$/,+,Exerciseprice,KT$/,Put-callparityrelatescallandputvaluestothevalueofaforwardcontract.Whenwewanttotalkaboutthevalue(ratherthanchangesinthevalue)ofalongcallandashortput,weneedtoadjustfortheexerciseprice.Thegeneralcaseiscalled“put-callparity”andrelatesthevalueofalongcall,ashortput,theexerciseprice,andtheforwardpriceatexpiration:CallTd/f-PutTd/f+Kd/f=FTd/f,Combinationsofoptions-AStraddleoption,Onepossiblespeculativestrategyforvolatilecurrenciesistopurchasebothaputoptionandacalloptionatthesameexerciseprice.Thisiscalledastraddle.Longstraddle=alongcallandalongputonthesameunderlyingassetandwiththesameexerciseprice.Shortstraddle=ashortcallandashortputonthesameunderlyingassetandwiththesameexerciseprice.,Combinationsofoptions-AStraddleoption,Heresanexample,Inearly1995,aroguetradernamedNickLessondrovedtheUnitedKingdomsBaringsBankintobankruptcythroughunauthorizedspeculationinNikkeistockindexfuturesontheSingaporeandOsakastockexchanges.LeesonsoldoptionstraddlesontheNikkeiindexatatimewhenvolatilityontheindexwaslow.LeesonformedashortstraddlebysimultaneouslysellingcallsandputontheNikkeiindex.Includingtheproceedsfromthesaleofthecallandtheput,theprofit/lossdiagramontheshortstraddlepositionatexpirationlookslikethis:,profit/lossonashortstraddle,HeplacedabetonthevolatilityoftheNikkeiindex.AslongastheNikkeiindexdidnotvarytoomuch,Leesonwouldhavewonhisbet.LeesonlosesiftheNikkeiindexrisestoohighorfallstoolow.Thefactwas:VolatilityontheNikkeiindexwaslowatthetimeLeesonsoldhisposition.Asitturnedout,theNikkeiindexfellbelowtheprofitablerange.,LeesonincurredfurtherlossesbybuyingfuturesontheNikkeiindexinthehopesofarecoverythat,toBaringsregret,neveroccurred.,TheDeterminantsofOptionValues,AmericancurrencyoptionspriortoexpirationpricedaccordingtotheBlack-Scholesmodelare:OptionvaluedeterminantCalld/fPutd/f1.Underlyingexchangerate(Sd/f)+-2.Exerciseprice(Kd/f)-+3.Risklessrateincurrencyd(id)+-4.Risklessrateincurrencyf(if)-+5.Timetoexpiration(T)+6.Exchangeratevolatilitys(sd/f)+Optionvalue=Timevalue+intrinsicvalue,IntrinsicValue,TimeValue&TotalValueforaCallOptiononBritishPoundswithaStrikePriceof$1.70/,1.69,1.70,1.71,1.72,1.73,1.68,1.67,1.66,0.0,1.0,2.0,3.0,4.0,5.0,Spotrate($/),OptionPremium(UScents/),3.30,5.67,4.00,6.0,1.74,1.67,Totalvalue,Intrinsicvalue,Timevalue,-Valuationonfirstdayof90-daymaturity-,0,IntrinsicValue,TimeValue&TotalValueforaCallOptiononBritishPoundswithaStrikePriceof$1.70/,TheIntrinsicValueofanOption,Theintrinsicvalueofanoptionisthevalueoftheoptionifitisexercisedtoday.Calloptionvaluewhenexercised=Max(std/f-kd/f),0Putoptionvaluewhenexercised=Max(kd/f-std/f),0ifacallorputoptionisout-of-money,itsintrinsicvalueiszero.Ifanoptionisin-the-money,itsintrinsicvalueisequaltothedifferencebetweentheexercisepriceandthevalueoftheunderlyingasset.,Ex,:ForSept1.60putoptiononBritish,Pound,spotrateis$1.5841,the,optionpremiumis$0.0220,compute,intrinsicvalueandtimevalue.,Intrinsicvalue,=X-S,=1.60-1.5841=$0.0159,Timevalue,=P-intrinsicvalue,=0.0220-0.0159=$0.0061,Thetimevalueofanoption,Timevalue=Optionvalue-intrinsicvalueIntrinsicvalue=valueifexercisedimmediatelyThetimevalueofacurrencyoptionisafunctionofthefollowingsixdeterminantsExchangerateunderlyingtheoptionExercisepriceorstrikingpriceRisklessrateofinterestidincurrencydRisklessrateofinterestifincurrencyfVolatilityintheunderlyingexchangerateTimetoexpirationThetwomostcriticalvariablesarevolatilityintheunderlyingexchangerateandthetimetoexpiration.,Thetimevalueofanoption,Timevalue=Optionvalue-intrinsicvalueAsexchangeratevolatilityincreases,thevaluesofAmericancallandputoptionsincrease.Asthetimetoexpirationincreases,thevaluesofAmericancallandputoptionsincrease.Thatis,Americanoptionvaluesaregreaterifvolatilityintheunderlyingassetincreasesorifthetimetoexpirationislonger.Becauseoptionholderscontinuetogainononesideoftheexercisepricebutdonotsuffercontinuedlossesontheotherside,optionsbecomemorevaluableastheend-of-periodexchangeratedistributionbecomesmoredispersed.,Thetimevalueofanoption,Asexpiration,onlythatportionoftheexchangeratedistributionthatexpiresin-the-moneyhasvalue.Theout-of-themoneycalloptionhaslittlevaluebecausethereislittlelikelihoodofthespotrateclimbingabovetheexerciseprice.Asthevariabilityofend-of-periodexchangeratesincreases,thereisanincreasingprobabilitythatthespotratewillcloseabovetheexerciseprice.Asthemoreout-of-themoneytheoptionis,thetimevalueissmaller.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。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。,Exchangeratevolatilityandout-of-the-moneycalloptionvalue,Thetimevalueofanoption,Anat-the-moneycalloptiongainsifthespotrateclosesfartherabove,theexercisepricebutdoesnotloseifthespotrateclosesfartherbelostheexerciseprice.Asthevariabilityofend-of-periodexchangeratesincreases,anareaofthedistributionfallsfartherin-the-moneyandtheoptionsismorevaluable.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50%。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，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。,Exchangeratevolatilityandat-the-moneycalloptionvalue,Thetimevalueofanoption,Forin-the-moneycalloption,ifanunderlyingexchangerateisbelowtheexercisepriceatexpiration,theoptionhaszerovalueregardlessofthehowfartheclosingpricefallsbelowtheexerciseprice.Ontheotherhand,asthespotrateincreases,thecalloptioncontinuestoincreaseinvalue.Thus,in-the-moneycalloptionsbenefitfromhighervolatility.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，立权人需要买入对应资产进行套期。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。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，当期权价内越多时，时间价值越小。,Exchangeratevolatilityandin-the-moneycalloptionvalue,IntrinsicValue,TimeValue&TotalValueforaCallOptiononBritishPoundswithaStrikePriceof$1.70/,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。,货币期权定价的敏感性分析,1.对即期汇率变化的敏感性（Delta）:Optionsdeltaisalsocalledthehedgeratio:thechangeinoptionpricewithrespecttoachangeinspotrate.（期权价格对即期汇率变化的敏感性称为Delta值）Ex:=20%,S=$0.72,C0=$0.0395.Ifspotratechangesto$0.71,C1=$0.0335,findtheDelta.Delta=C/S=(0.0395-0.0335)/(0.72-0.71)=$0.6该结果表明：如果给定Delta值0.6，那么，即期汇率变化1美分（$0.01/）,期权费变化将是0.60.010.006$。如果初始期权费是$0.0395/,即期汇率减少1美分（从$1.72/减少到$1.71/），则新的期权费就应该为$0.0395-$0.006=$0.0335/一般地，看涨期权的