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BusinessandOptionValuation[對(duì)應(yīng)中文教材2008年財(cái)務(wù)成本管理第十章:企業(yè)價(jià)值評(píng)估、第十一章:期權(quán)估價(jià)]

mainfeaturesofoptions(期權(quán)的主要特征)

Anoptiongivesitsholdertheright(butnottheobligation)tobuyorsellaspecificquantityofaspecificassetatafixedpriceonorbeforeaspecifiedfutureoptionispurchasedbytheoptionholderandissoldbytheoption‘writer’.

期權(quán)是指一種合約,該合約賦予持有人在某一特定日期或該日之前的任何時(shí)間以固定價(jià)格購進(jìn)或售出一種資產(chǎn)的權(quán)利。Exchange-tradedandOTCoptions

OptionsmightbeboughtandsoldonanoptionsexchangesuchasLIFFE[LONDONINTERNATIONALFINANCIALFUTURESEXCHANGE:倫敦國際金融期貨交易所],orarranged‘over-the-counter’[場(chǎng)外交易]withaoptionsincludeoptionsonequitysharesandoptionsonfuturescurrencyoptionsarealsoexchangetraded,forexampleonthePhiladelphiaStockExchange[費(fèi)城交易所].Interestrateoptionsandmostcurrencyoptionsareover-the-counter(OTC)options.

Afeatureofexchange—tradedoptionsisthat,likefuturescontracts,theyarestandardizedinstruments.[標(biāo)準(zhǔn)化的工具]

OTCoptions,incontrast,aretailoredtothespecificrequirementsoftheoptionbuyer.

Callsandputs

Optionsareeithercalloptionsorputoptions(oracombinationofacallandaput).

Acalloptiongivesitsholdertheright,butnottheobligation,tobuytheunderlyingitematthespecifiedprice.

Calloption:買入選擇權(quán);買入期權(quán);看漲期權(quán);

Aputoptiongivesitsholdertheright,butnottheobligation,toselltheunderlyingitematthespecifiedprice.

Putoption:賣出選擇權(quán);賣出期權(quán);看跌期權(quán);

Anoptionisacontractualtheholder(持有者)ofanoptionexercise(行使權(quán)利)theoption,thesellerorwriter(與seller)oftheoptionmustfulfillhissideofthecontract,andsell(calloption)orbuy(putoption)theunderlyingitem(期權(quán)的標(biāo)的資產(chǎn))attheagreedprice.Expirydate:European-styleandAmerican-styleoptions(歐式和美式)

Strikepriceorexerciseprice[執(zhí)行價(jià)格]

In-the-money(賺錢)[實(shí)值狀態(tài),溢價(jià)狀態(tài)]andout-of-the-moneyoptions(賠錢)[虛值狀態(tài),折價(jià)狀態(tài)]

Atthemoney(照所付的代價(jià))[平價(jià)期權(quán),平價(jià)狀態(tài)]

Anoptionwillonlyeverbeexercisedifitisin-the-money.

Optionpremium[期權(quán)價(jià)格/成本]

Anoptionispurchasedbythebuyerfromtheoptionsellerorpurchasepriceiscalledtheoptionpremium.

Apositioninoptionscanbeopenedbybuyingoptionstoholdalongpositionorsellingoptionstocreateashortlongorshortpositioncanbeheldineithercallsorputs.Thevalueofanoption[期權(quán)價(jià)值](itspremiumorcurrentmarketvalue)issaidtoconsistoftwoelements:

Intrinsicvalue[內(nèi)在價(jià)值]

Timevalue[時(shí)間溢價(jià)]

Intrinsicvalueisthedifferencebetweenthestrikepricefortheoptionandthecurrentmarketpriceoftheunderlyingitem.[內(nèi)在價(jià)值的大小,取決于期權(quán)標(biāo)的資產(chǎn)的現(xiàn)行市價(jià)與期權(quán)執(zhí)行價(jià)格的高低.]Onlyanin-the-moneyoptionhasanintrinsicvalue,valuecannotbenegative,soanout-of-the-moneyoptionhasintrinsicvalueof0.

Timevalueisthevalueplacedontheoption.[期權(quán)的時(shí)間溢價(jià)是指期權(quán)價(jià)值超過內(nèi)在價(jià)值的部分]

Timevaluedependsonfactorssuchas:

Theperiodoftimeremainingtotheoption'sexpirydate.[到期期限]

Thevolatilityofthemarketpriceoftheunderlyingitem.[股票價(jià)格的波動(dòng)率]

Foranout-of-the-moneyoption,theextenttowhichtheunderlyingmarketpricemustmovebeforetheoptionbecomesin-the-money.

pricing[期權(quán)定價(jià)]

Valueofacalloption[看漲期權(quán)]

Themajorfactorsindeterminingthepriceofacalloptionareasfollows:

Thepriceoftheunderlyinginstrumentandtheexercise,itisthedifferencebetweenthestrikepriceandtheunderlyingmarketpricethatmatters.[期權(quán)標(biāo)的物的價(jià)格和執(zhí)行價(jià)格]Thehigherthepriceoftheunderlyinginstrument,themorevaluablethecalloption,andthelowertheexercisepricethemorevaluablethecalloptionThetimetogotolongertheremainingperiodtoexpiry,thegreatertheprobabilitythattheunderlyinginstrumentwillriseinvalue.[距離到期日時(shí)間]

Thevolatilityoftheunderlyinggreaterthevolatilityofthepriceoftheunderlyinginstrumentthegreatertheprobabilityoftheoptionyieldingisanotheraspectofthetimevalueofanoption.[期權(quán)標(biāo)的價(jià)格的變動(dòng)]

Interestrates[利率]

WhetheraEuropeanoptionoranAmericanoption.[歐式還是美式]

TheBlack-Scholesoptionpricingmodel[布萊克——斯科爾斯期權(quán)定價(jià)模型]

LctPs=thepriceoftheunderlyinginstrument,c,currentsharepriceifpricinganequitycalloption

N(di)=theprobabilitythatanormaldistributionislessthandistandarddeviationsabovethemean

X=theexerciseprice

r=theriskfreeinterestrate.(NBQuotethisasanannualrateasadecimalnumber)

T=thetimetoexpiry(againquotedinyears),sothatforasix-monthoptionTandforathree-monthoption

σ=thestandarddeviationoftheunderlyinginstrument’sreturns

ThenthebasicformoftheBlack-ScholesmodelgivesthevalueofaEuropeancalloptionas;

Example

Solution

Firstwecalcutated1andd2,

Wearegiventhevarianceofreturnsontheshare,sotakethesquareroottogetthestandarddeviation.

Roundthisto(twodecimalplaces)

Havingcalculatedvaluesford1andd2,wecannowgoontocalculatetheoptionprice,

Optioionprice=()×××N()

(usingacalculator).

ToestablishthevalueofN(d1)when,refertothenormaldistributiontables.

ThisshowsavalueofSinced1isgreaterthan0,andtoget,Inthecalculationbelow,thisisroundeddownto.

Similarly,tocalculateavalueforN(d2),when,welookupthevalueofinthenormaldistributiongivesus.Thisisroundeddowntointhefollowingpricecalculation.

Youmightliketoseethenormaldistributioncalculationshowngraphically.

SoN()=+=

Assetvaluationbases

Thenetassetsvaluationmethodcanbeusedasoneofmanyvaluationmethods,ortoprovidealowerlimitforthevalueofacompany.Byitselfitisunlikelytoproducethemostrealisticvalue.Choiceofvaluationbases

Possibilitiesinclude:

Historicbasis

Replacementbasis

Realizablebasis

basedvaluationbases

P/Eratiosareusedwhenalargeblockofshares,orawholebusiness,isbeingvalued.Thismethodcanbeproblematicwhenquotedcompanies’P/Eratiosareusedtovalueunquotedcompanies.TheP/Eratio(earnings)methodofvaluation

Thisisacommonmethodofvaluingacontrollinginterestinacompany,wheretheownercandecideondividendandretentionspolicy.TheP/Eratiorelatesearningspersharetoashare'svalue.

SinceP/Eratio=Marketvalue/EPS

thenmarketvaluepershare=EPS×P/Eratio

Earningspershare(EPS)

=profit/lossattributabletoordinaryshareholders/weightedaveragenumberofordinaryshares

Theearningsyield[盈余報(bào)酬率,市盈率priceearningratio的倒數(shù)]valuationmethod

Anotherincomebasedvaluationmodelistheearningsyieldmethod.

ThismethodiseffectivelyavariationontheP/Emethod(theEYbeingthereciprocaloftheP/Eratio),usinganappropriateearningsyieldeffectivelyasadiscountratetovaluetheearnings:

Wecanincorporateearningsgrowthintothismethodinthesamewayasthegrowthmodel.

Thisformulaisgivenonyourformulasheetas

flowbasedvaluationmodels

Thedividendvaluationmodel-

Thedividendvaluationmodelisbasedonthetheorythatanequilibriumpricefor[均衡價(jià)格]anyshare(orbond)onastockmarketis:

Thefutureexpectedstreamofincomefromthesecurity

Discountedatasuitablecostofcapital

Equilibriummarketpriceisthusapresentvalueofafutureexpectedincomestream.Theannualincomestreamforashareistheexpecteddividendev

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