版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
——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第1页/共53页第一页,共54页。——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第2页/共53页第二页,共54页。
ChapterOverviewWhatisanoptionOptionpayoffprofilesCombinationsofoptionsThedeterminantsofcurrencyoptionvaluesHedgingwithcurrencyoptions第3页/共53页第三页,共54页。AforwardobligationSupposeaU.S.companyhasaforwardobligationof£1milliondueattimeTinfourmonths.CurrentspotandforwardratesareS0$/£=FT$/£=$1.45/£.TheexpectedamountdueonthisforwardobligationisE[CFT$]=(E[CFT£])(E[ST$/£])=(£1,000,000)($1.45/£)=$1,450,000.Iftheactualexchangerateis$1.50/£,thenthis£1millionobligationwillcostCFT$=(CFT£)(ST$/£)=(£1,000,000)($1.50/£)=$1,500,000.Inthiscase,theU.S.companyhasanunexpectedlossof$50,000.
Underlyingtransaction-£1,000,000CurrencyexposureDV$/£DS$/£第4页/共53页第四页,共54页。AforwardhedgeThisforwardexposurecanbehedgedbybuyingpoundsterlingintheforwardmarket,whichinthiscasemeanssimultaneouslysellingdollarsforward.Buy£1millionintheforwardmarketattheforwardpriceF1$/£=$1.45/£ThecashflowtimelineandthepayoffprofileoftheforwardcontractareshownontheslidebasedontheforwardrateofexchangeisFT$/£=$1.45/£.-IftheactualexchangerateisST$/£=$1.50/£,thenpurchasing£1,000,000attheforwardpriceofFT$/£=$1.45/£willsaveyou$50,000andoffsetyourlossontheunderlyingexposure.-Conversely,ifthepoundfallsto$1.40/£,youwillgain$50,000ontheunderlyingobligationbutlose$50,000ontheforwardcontract.第5页/共53页第五页,共54页。AforwardhedgeWouldn’titbenicetoownaninsurancepolicyagainstariseintheexchangeratewithoutacorrespondinglossifexchangeratesfall?Longpoundforward+£1,000,000-$1,450,000ExposureofforwardcontractDV$/£DS$/£第6页/共53页第六页,共54页。AnoptionhedgeAcurrencyoptionislikeone-halfofaforwardcontracttheoptionholdergainsifpoundsterlingrisestheoptionholderdoesnotloseifpoundsterlingfallsLongpoundcall(optiontobuypoundsterling)DS$/£DV$/£第7页/共53页第七页,共54页。AnoptionhedgeOptionsareusedfortwopurposes:HedgingSpeculation Hedgingisbyfarthemorecommonusebycorporatefinancialmanagers.Inthisexample,acalloptiononpoundsterlingactsasaninsurancepolicy(ahedge)againstariseinthevalueofthepound.IftheactualexchangeraterisestoST$/£=$1.50/£atexpiration,thentheoptionprovidesapayoffof(£1,000,000)($0.05/£)=$50,000.IftheactualexchangeratefallstoST$/£=$1.40/£,thentheoptionisout-of-the-moneyandisnotexercised.Ofcourse,thisinsurancepolicydoesnotcomefree.
Thecostoftheoptioniscalledtheoptionpremium.Theoptionholderpaystheoptionpremiumwhentheoptionispurchased.第8页/共53页第八页,共54页。OptionsContracts:PreliminariesAforeigncurrencyoptionisacontractgivingtheoptionpurchaser(thebuyer)theright,butnottheobligation,tobuyorsellagivenamountofforeignexchangeatafixedpriceperunitforaspecifiedtimeperiod(untilthematuritydate).Thebuyerofanoptionistermedtheholder,whiletheselleroftheoptionisreferredtoasthewriterorgrantor.Everyoptionhasthreedifferentpriceelements:Theexerciseorstrikeprice–theexchangerateatwhichtheforeigncurrencycanbepurchased(call)orsold(put)Thepremium–thecost,price,orvalueoftheoptionitselfTheunderlyingoractualspotexchangerateinthemarket第9页/共53页第九页,共54页。OptionsContracts:PreliminariesAnoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanassetinthefuture,atpricesagreedupontoday.Callsvs.PutsCalloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.第10页/共53页第十页,共54页。OptionsContracts:PreliminariesEuropeanvs.AmericanoptionsEuropeanoptionscanonlybeexercisedontheexpirationdate.Americanoptionscanbeexercisedatanytimeuptoandincludingtheexpirationdate.Sincethisoptiontoexerciseearlygenerallyhasvalue,AmericanoptionsareusuallyworthmorethanEuropeanoptions,otherthingsequal.第11页/共53页第十一页,共54页。OptionsContracts:PreliminariesIntrinsicValueThedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.SpeculativeValueThedifferencebetweentheoptionpremiumandtheintrinsicvalueoftheoption.OptionPremium=IntrinsicValueSpeculativeValue+第12页/共53页第十二页,共54页。CurrencyOptionsMarketsPHLX(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.第13页/共53页第十三页,共54页。PHLXCurrencyOptionSpecificationsCurrencyContractSizeAustraliandollarAD50,000Britishpound£31,250CanadiandollarCD50,000Euro€62,500Japaneseyen¥6,250,000SwissfrancSF62,500第14页/共53页第十四页,共54页。ForeignCurrencyOptionsStatusofanoption a. In-the-money
Call: Spot>strike Put: Spot<strike
b. Out-of-the-money
Call: Spot<strike Put: Spot>strike
c. At-the-money
Spot=thestrike第15页/共53页第十五页,共54页。
CurrencyFuturesOptionsAre
anoptiononacurrencyfuturescontract.Exerciseofacurrencyfuturesoptionresultsinalongfuturespositionfortheholderofacallorthewriterofaput.Exerciseofacurrencyfuturesoptionresultsinashortfuturespositionforthesellerofacallorthebuyerofaput.第16页/共53页第十六页,共54页。
ThefunctionsofCallOptionFirmsmaypurchasecurrencycalloptionstoTheymaypurchasecurrencycalloptionstohedgefuturepayables;tohedgepotentialexpenseswhenbiddingonprojects;andtohedgepotentialcostswhenattemptingtoacquireotherfirms.Speculatorsmaypurchasecalloptionsonacurrencythattheyexpecttoappreciate.
Profit=selling(spot)price–optionpremium–buying(strike)priceTheymayalsosell(write)calloptionsonacurrencythattheyexpecttodepreciate.Profit=optionpremium–buying(spot)price+selling(strike)price第17页/共53页第十七页,共54页。BreakevenonCallOptionThepurchaserofacalloptionwillbreakevenwhensellingprice=buying(strike)price+optionpremiumTheseller(writer)ofacalloptionwillbreakevenwhen
buyingprice=selling(strike)price+optionpremiumESTProfitloss–c0E+c0LongcallESTProfitlossc0E+c0short1call第18页/共53页第十八页,共54页。ThefunctionsofPutOptionFirmsmaypurchasecurrencyputoptionstohedgefuturereceivables.Speculatorsmaypurchaseputoptionsonacurrencythattheyexpecttodepreciate.
Profit=selling(strike)price–buyingprice–optionpremiumTheymayalsosell(write)putoptionsonacurrencythattheyexpecttoappreciate.
Profit=optionpremium+sellingprice–buying(strike)price第19页/共53页第十九页,共54页。ESTProfitloss–p0E–p0longputE–p0ESTProfitp0E–p0shortput–E+p0BreakevenonPutOptionThepurchaserofaputoptionwillbreakevenwhenbuyprice=selling(strike)price-optionpremiumTheseller(writer)ofaputoptionwillbreakevenwhen
sellingprice=buying(strike)price-optionpremium第20页/共53页第二十页,共54页。PayoffprofileofacalloptionatexpirationLongcallShortcallST$/£CallT$/£KT$/£ST$/£-CallT$/£KT$/£In-the-moneyOut-of-the-moneyOut-of-the-moneyIn-the-moneyCurrencyoptionsareazero-sumgame;
gainsononesideareoffsetbylossesontheother.第21页/共53页第二十一页,共54页。PayoffprofileofaputoptionatexpirationShortputKT$/£LongputST$/£PutT$/£ST$/£-PutT$/£KT$/£In-the-moneyOut-of-the-moneyOut-of-the-moneyIn-the-moneyAsinthepreviousslide,optionsareazero-sumgame;gainsononesideareoffsetbylossesontheother.第22页/共53页第二十二页,共54页。Forwards,puts,andcalls
——AForwardbyAnyOtherNameAcombinationofalongcallandashortputatthesameexercisepriceandwiththesameexpirationdateresultsinalongforwardpositionatthatforwardpriceDST$/£DCallT$/£DFT$/£-DPutT$/£DST$/£DST$/£LongcallShortputLongforward+=第23页/共53页第二十三页,共54页。Forwards,puts,andcalls
——AForwardbyAnyOtherNameConversely,ashortcallandalongputwiththesameexercisepriceandexpirationdateisequivalenttoashortforwardposition.DST$/£-DCallT$/£-DFT$/£DPutT$/£DST$/£DST$/£ShortcallLongputShortforward+=第24页/共53页第二十四页,共54页。AForwardbyAnyOtherName:
Put-callparityLongforward=FT$/£ST$/£-PutT$/£ST$/£Shortput+ST$/£CallT$/£LongcallKT$/£ST$/£+ExercisepriceKT$/£Put-callparityrelatescallandputvaluestothevalueofaforwardcontract.Whenwewanttotalkaboutthevalue(ratherthanchangesinthevalue)ofalongcallandashortput,weneedtoadjustfortheexerciseprice.Thegeneralcaseiscalled“put-callparity”andrelatesthevalueofalongcall,ashortput,theexerciseprice,andtheforwardpriceatexpiration:
CallTd/f-PutTd/f+Kd/f=FTd/f第25页/共53页第二十五页,共54页。
Combinationsofoptions
-AStraddleoptionOnepossiblespeculativestrategyforvolatilecurrenciesistopurchasebothaputoptionandacalloptionatthesameexerciseprice.Thisiscalledastraddle.Longstraddle=alongcallandalongputonthesameunderlyingassetandwiththesameexerciseprice.Shortstraddle=ashortcallandashortputonthesameunderlyingassetandwiththesameexerciseprice.KTSTSTKTVTVTLongstraddleShortstraddle第26页/共53页第二十六页,共54页。
Combinationsofoptions
-AStraddleoptionHere´sanexample,Inearly1995,aroguetradernamedNickLessondrovedtheUnitedKingdom´sBaringsBankintobankruptcythroughunauthorizedspeculationinNikkeistockindexfuturesontheSingaporeandOsakastockexchanges.LeesonsoldoptionstraddlesontheNikkeiindexatatimewhenvolatilityontheindexwaslow.LeesonformedashortstraddlebysimultaneouslysellingcallsandputontheNikkeiindex.Includingtheproceedsfromthesaleofthecallandtheput,theprofit/lossdiagramontheshortstraddlepositionatexpirationlookslikethis:第27页/共53页第二十七页,共54页。profit/lossonashortstraddleSTNikkeiKTNikkeiVTNikkeiHeplacedabetonthevolatilityoftheNikkeiindex.
AslongastheNikkeiindexdidnotvarytoomuch,Leesonwouldhavewonhisbet.
LeesonlosesiftheNikkeiindexrisestoohighorfallstoolow.
Thefactwas:VolatilityontheNikkeiindexwaslowatthetimeLeesonsoldhisposition.Asitturnedout,theNikkeiindexfellbelowtheprofitablerange.LeesonincurredfurtherlossesbybuyingfuturesontheNikkeiindexinthehopesofarecoverythat,toBaring´sregret,neveroccurred.第28页/共53页第二十八页,共54页。
TheDeterminantsofOptionValuesAmericancurrencyoptionspriortoexpirationpricedaccordingtotheBlack-Scholesmodelare: Optionvaluedeterminant Calld/f Putd/f1. Underlyingexchangerate(Sd/f) + -2. Exerciseprice(Kd/f)- +3. Risklessrateincurrencyd(id) + -4. Risklessrateincurrencyf (if) - +5. Timetoexpiration(T) + +6.Exchangeratevolatilitys(sd/f) +
+Optionvalue=Timevalue+intrinsicvalue第29页/共53页第二十九页,共54页。IntrinsicValue,TimeValue&TotalValueforaCallOptiononBritishPoundswithaStrikePriceof$1.70/£
第30页/共53页第三十页,共54页。1.691.701.711.721.731.681.671.660.01.02.03.04.05.0Spotrate($/£)OptionPremium(UScents/£)3.305.674.006.01.741.67TotalvalueIntrinsicvalueTimevalue--Valuationonfirstdayof90-daymaturity--0
IntrinsicValue,TimeValue&TotalValueforaCallOptiononBritishPoundswithaStrikePriceof$1.70/£第31页/共53页第三十一页,共54页。TheIntrinsicValueofanOptionTheintrinsicvalueofanoptionisthevalueoftheoptionifitisexercisedtoday.Calloptionvaluewhenexercised=Max[(std/f-kd/f),0]Putoptionvaluewhenexercised=Max[(kd/f-std/f),0]ifacallorputoptionisout-of-money,itsintrinsicvalueiszero.Ifanoptionisin-the-money,itsintrinsicvalueisequaltothedifferencebetweentheexercisepriceandthevalueoftheunderlyingasset.
第32页/共53页第三十二页,共54页。Ex:ForSept1.60putoptiononBritishPound,spotrateis$1.5841,theoptionpremiumis$0.0220,computeintrinsicvalueandtimevalue.
Intrinsicvalue=X-S=1.60-1.5841=$0.0159Timevalue=P-intrinsicvalue=0.0220-0.0159=$0.0061第33页/共53页第三十三页,共54页。
ThetimevalueofanoptionTimevalue=Optionvalue-intrinsicvalueIntrinsicvalue=valueifexercisedimmediatelyThetimevalueofacurrencyoptionisafunctionofthefollowingsixdeterminantsExchangerateunderlyingtheoptionExercisepriceorstrikingpriceRisklessrateofinterestidincurrencydRisklessrateofinterestifincurrencyfVolatilityintheunderlyingexchangerateTimetoexpirationThetwomostcriticalvariablesarevolatilityintheunderlyingexchangerateandthetimetoexpiration.第34页/共53页第三十四页,共54页。ThetimevalueofanoptionTimevalue=Optionvalue-intrinsicvalue
Asexchangeratevolatilityincreases,thevaluesofAmericancallandputoptionsincrease.Asthetimetoexpirationincreases,thevaluesofAmericancallandputoptionsincrease.Thatis,Americanoptionvaluesaregreaterifvolatilityintheunderlyingassetincreasesorifthetimetoexpirationislonger.Becauseoptionholderscontinuetogainononesideoftheexercisepricebutdonotsuffercontinuedlossesontheotherside,optionsbecomemorevaluableastheend-of-periodexchangeratedistributionbecomesmoredispersed.第35页/共53页第三十五页,共54页。ThetimevalueofanoptionAsexpiration,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。第36页/共53页第三十六页,共54页。Exchangeratevolatilityandout-of-the-moneycalloptionvalue
CallTd/fSTd/fSTd/f
CallTd/fSTd/fSTd/f第37页/共53页第三十七页,共54页。
ThetimevalueofanoptionAnat-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。第38页/共53页第三十八页,共54页。Exchangeratevolatilityandat-the-moneycalloptionvalue
CallTd/fSTd/fSTd/f
CallTd/fSTd/fSTd/f第39页/共53页第三十九页,共54页。ThetimevalueofanoptionForin-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。第40页/共53页第四十页,共54页。Exchangeratevolatilityandin-the-moneycalloptionvalue
CallTd/fSTd/fSTd/f
CallTd/fSTd/fSTd/f第41页/共53页第四十一页,共54页。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。第42页/共53页第四十二页,共54页。
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):
Option‘sdeltaisalsocalledthehedgeratio:
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($0.01/£),期权费变化将是0.6×0.01=0.006$。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=$0.0335/£一般地,看涨期权的Delta值变化在+1和0之间。而看跌期权的Delta值变化在-1和0之间第43页/共53页第四十三页,共54页。交易者根据Delta值对期权分类Thehigherthedelta,thegreatertheprobabilityoftheoptionexpiringin-the-money。当期权朝实值期权变化时,Delta值就上升趋向于1.0;当期权朝虚值期权变化时,Delta值就下降趋向于0;
看涨期权费的分解协定价格($/£)即期价格看涨期权费内在价值时间价值(美分/£)=(美分/£)+(美分/£)Delta值1.701.701.701.751.701.656.375.001.373.300.003.301.370.001.370.710.500.28第44页/共53页第四十四页,共54页。2.离到期日的时间(theta)期权的价值随离到期日的时间长度而增加,预期期权费的变化与到期日时间变化的比值称为Option‘stheta:thechangeinoptionpricewithrespecttoa
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 2025年中国婴童服饰行业市场深度研究及投资策略研究报告
- 2025年中国避光输液器行业发展前景预测及投资方向研究报告
- 2024物联网应用平台开发与部署合同
- 2021-2026年中国化工包装行业发展监测及投资战略规划研究报告
- 2025年中国关节置换手术机器人行业市场深度研究及投资战略规划报告
- 2024中国饮料及茶叶批发市场前景及投资研究报告
- 2021-2026年中国藿香正气制剂行业发展监测及投资战略规划研究报告
- 和环境保护2024年投资备选项目可行性研究报告编制
- 2025年销售合同绩效评估补充协议书3篇
- 2025年度学校教育设施大理石地板铺设合同3篇
- 拆迁评估机构选定方案
- 床旁超声监测胃残余量
- 上海市松江区市级名校2025届数学高一上期末达标检测试题含解析
- 综合实践活动教案三上
- 《新能源汽车电气设备构造与维修》项目三 新能源汽车照明与信号系统检修
- 2024年新课标《义务教育数学课程标准》测试题(附含答案)
- 医院培训课件:《静脉中等长度导管临床应用专家共识》
- 趣味知识问答100道
- 中国国际大学生创新大赛与“挑战杯”大学生创业计划竞赛(第十一章)大学生创新创业教程
- 钢管竖向承载力表
- 2024年新北师大版八年级上册物理全册教学课件(新版教材)
评论
0/150
提交评论