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1、MorganStan1.eyQuantFinance笔试来源：王汉宁的日志校内上有一篇被痛转的日志“你有去华尔街的资格么”，说的就是我标题里的这个项目。他们的聘请现在有了笔试,今日刚笔完这个，吐血，离”去华尔街的资格”还有好远，权当练习九.90分钟100道单选，4选1,选错了扣1/4的分.不让用计算器，所以遇到神马1.n(2),正态分布各种区间点这种东西之前没记过就无比蛋疼。假如不是学问非常全面且娴熟度如同高考，应当很难做完吧。而I1.据说有A,B,CD四套题，我没看我的是哪套。几套题之间有交叉,感觉他们应当是有个题库随机出的四套吧“现在把我还记得的题目(尽然能回忆出一大半！)贴出来供大家消遣
2、，有些题目没看懂，有的也没记住，所以难免有叙述不清的状况，凑合看吧。许多不会的题各位大牛指导。Cii1.cu1.us1. (x+2y)在平面上两条曲线间的积分,没记住2. int(0,pi12)of(cos-sinx)/(sinx+cosx)还是神马的3. Extrcmaoff(x)=x2+1.x4. DerivativeofxInx5. Derivativeofcos(x*2)6. x(t)=ax+by,y(t)=cx+y,(forgotcoefficients).x(0)=4,y(0)=3,x(I)?(Maybeneedtoso1.vetwoODEsanddeterminecoeffici
3、ents?)7. Fastestgrowingdirectionoff(x)=1.(1.+ax2+by2+cz2)at(1,1,-2)8. int(0,inf)OfeXP(Xa2/2)也可能是我看错题了是exp(r22)9. SimiIartothequestion:Whatistheintersectionvo1.umeoftwounitCy1.inder?1.inearA1.gebra1. 解二元次方程组。2. Underwhichsituationwi1.1.a1.inearsystemhasnoso1.utions.3. 6variab1.e.3equation,ingenera1.h
4、owmanydimsdotheso1.utionshave?4. (Cartrememberc1.ear1.y)Positivedefinitematrix4pi1.es,13ineach.2Acosinonepi1.e,theother2cesintwodifferentpi1.es,therestpi1.edoesnIhaveanAce.Prob?4. X,Y,Zhaveequa1.corr,theIOWCrboundofthiscorr?(-0.5)5. Randomvariab1.eX,Y,Z,corr(X,Y)=corr(Y,Z)=c0,Whatistheminimumcorre1.
5、ationbetweenXandZ?(2c21)6. Givendataandsomestatistics,whatistheregressionfunction?7. Uniformdistribution,MI.EestimatorofainU0,a(n+1.)n*max(xi)8. 10000coins,probofmorethan4950heads?(1-N(-1)9. 100coins,probofmorethan60heads?(I-N(-2)10. 100uniformvariab1.es,.anothercentra1.1imittheoryquestion11. 18sock
6、s,12inoneco1.or,6intheotherco1.or,probofpick2toformapair?12. Picking2from52pokercards,probofapair?13. Xhave0meanand1var,E(x+2)2?14. X1Yhave0meanand1var,E(XX+Y=1.)?orundetermined?15. Fi1.1.inb1.ank:X1.X2areiid.ifforanya,bwecanfindc,dsothataX1.+bX2hassamedistributionofcX+d,thenthedistributionis:norma1
7、.,Poisson,stab1.e,(forgotthe1.astchoice)16. Twopeop1.e(onefromHarvardandonefromMIT.)arriveuniform1.ybetween12pm-1.pn,theprobofonepersonwaitinganotherfor1.essthan15min?(1/4,1/8,16,.绿皮书)17. Distributionofsamp1.evo1.ati1.itydividedbysamp1.emean?(chi-square,gamma,F,t)18. Modeof(11,11,29,41,41,41)19. Sta
8、ndarddiviationof(11,11,29,41,41,41)20. 25peop1.eareassignedseatsbuttheysittedrandom1.y,whatistheexpectednumberofpeop1.ehavingorigina1.assignedseats:1,5,25?StochasticProcess&MathFinance1. ExpectedtimeforWtiohitboundary+-1(1)2. GivenzerobondpriceP(0,T)=1.(1.+T2),forwardratebetween(T1.,T2)?3. Anasset,(
9、fo1.1.owingGBM?)has$0do1.1.arva1.uenow,$1inayear,whatisthepriceat1.=0.5:0.5(0.5),0.5(0.75),0.5,0.5(1.25)?4. Radon-Nikodymderivativefromrea1.probmeasuretoforwardmeasure,withrespectiveofbondpriceP(0,t)5. TwoindependentBrownianmotion(Bt,Wt),startingatpoint(1,1),whatistheProbabiIityofthiscurvehi1.1.ingp
10、ositiveX-UXiSbeforehittingnegativeX-axis?(3/4)6. (Can1.rememberc1.ear1.y)GiventheprocessGBM(r,signa?)ofUSD/GBPpriceinUSDriskneutra1.measure,whatistheGBP/USDinGBP?Driftterminchoicesare(-r,-r-sigma_2,-r+sigma-2)7. dudt-5u=0,backwardEu1.er-method.whatchoicesofdtcanmakeUunstab1.e:3,5,8,11,(Cantrememberc
11、1.ear1.y)ora1.1.above?8. X=exp(Wt)1EXatt=2?(e)9. Stockpricefo1.1.owsGBM1r=0.05,sigma=0.3,spot=100,probofprice50inoneyearfromnow?10. Binaryca1.1option,Europeanprice=0.1,Americanprice:0.1,0.2,0.3,0.411. Twoequiva1.entmeasure,PandP,P（八）=0.5,P(,)=?(0,1)12. Thespotis10,ifyouthinkone-month1.ater,thepricew
12、i1.1.be8and10withequa1.probabi1.ity,risk-freeinterestrateis5%,whatisthepriceofca1.1.optionstrikeat10?(between5/1.05and10/1.05becauseofrisk-freeprobabi1.ity.)13. Gaussiancopu1.a:hazardrateofandBare1%and2%.contractpayyou$1ifAdefau1.tsear1.ierthanB.Thepriceofthecontracthas1.owestpricewhenthecorre1.atio
13、nis(0,75%,100%,.)?14. MonteCar1.o:tofindoutthemeanofA,findavariab1.eB,corr(AtB)=c,andsimu1.ate+B(E(B)-B)insteadof.WhatisB?(cov(a,b)var（八）,cov(a,b)/var(b),1,-1)15. MonteCar1.o;needtosimu1.atesomerareevent,soUneedtosimu1.ateinadifferentmeasure.Whatisthenameofthistechnique?(sequentia1.resamp1.ing?)16.
14、Varianceofint(t1.,t2)ofWt_2dWt,andsomeotherito,Sintegra1.prob1.ems17. Dividend-payingstock(discretedividend),thepricedifferenceofInode1.inginGBMandjumpdiffusionFinance(FIandoptions)1. Bond:5%coupon,(IOyear?)1000face,6%yie1.d,price?2. Bond:3%coupon10yearbondtradedatpar(100),Whatisthepriceifrategoesup
15、1.bp:(99.91,99.99,100.01,.)3. Whichishigher?FRvs.Eurodo1.1.arfutures4. At2009,atraderbe1.ievesthatdividendin2011is1.owerthanexpectation,strategy?1.ong/short2010forwardand1.ong/short2011forward?5. (Can,trememberc1.ear1.y)Atraderobservedthatimp1.iedvo1.ofOTMca1.1.sandputsarehigherthanthatofTMoption,st
16、rategy:ca1.endarspread,bu1.1.spread,bearspread,but1.er11y?(1guessedbutterf1.y.)6. IfassetpricePoSitiVCcorre1.atedwithinterestrate,futurepriceishigher/1.owerthanforwardprice?(higher)7. Ifinterestrateisdetenuinistic,futurepriceishigher/1.owerthanforwardprice?(equa1.)8. 1.ong1.ong-termTMca1.1.andshorts
17、hort-termATMca1.1.,adjusttheratiotomaketota1.vegazero.Ifbeforeexpiryoftheshort-termoption,spot=strikeagain,vega:positive,negative,zero?(positive?)9. Thetraderwantstodoade1.ta-hedgestrategy,buthep1.ugswrongSigmaDimp1.iedvo1.,assumetheportfo1.iois-C+de1.ta*S,whatwi11thePOrIfo1.iova1.uechange?whenthest
18、ockincrease(iecrease,theVaIUei11creasedecrease.10. Binaryoption,increaseofde1.1.a:(positive,negative,itdepends,.)U.Thetaisthepartia1.derivativeof(time)12. WhichoftheCOIIOWingisnotB1.ackScho1.esassumption:(freeborrowand1.endingatrisk-freerate,notransactioncost,sametaxrate?.)13. Vo1.ati1.itysurface:on
19、thestrikedimensionisf1.at,ontheotherdimension,thevo1.shapeis:1)increasingfunctionofstrike2)decreasingwithstrike3)frown4)smi1.e14. (Can,trememberc1.ear1.y)ConditionofAmCriCanca1.1.beingexercised(IforgotwhetherdiVidend=Oornot)15. Adefau1.tprotectionseiIeris1.ong/shortcreditrisk16. Tohedgeinterestrater
20、iskof7yearbondof100MM,youneedtoshort2yearbondof?350MM?Programming1. Theformatof*ca1.1.edin*coutt(aninteger?Iforgot).*,1.ike*Ostreamfcoperator(OStreaout,Tc)”?2. staticmemberinitia1.ization:simp1.ecase(choosetheoneinitia1.izedoutofthec1.ass)3. staticmemberinitia1.ization:Intemp1.atec1.ass,howmanyinsta
21、nces?1) Cannothavestaticmemberintemp1.atec1.ass2)on1.yoneinstance3)asmanyasinstancesofc1.asses4)asmanyasinstantiationsofc1.asses4. staticmemberinitia1.ization:mu1.ti-threadcase5. 32-puter,non-OPIimiZedcode:Uin1.-32a=16,c=32,Q:Prinft(飞(T)ofunsignedint（八）-unsignedint(c):0,8,16,32?6. spaceneededtostore
22、thenumber1,000,000?17,18,19,20?(20?)7. Timecomp1.exityofmergesort?(0(n1.ogn)8. (Can*trememberc1.ear1.y)Binarytreesearchingtimewithrespectofn?9. Howmanycomparisonsareneededtosort5e1.ements?(4)10. Searchingin10,OOOdatacostsIns,100,000data?(10,35,100,350)11. Cannotusein:string,vector,1.ist,.(1.ist)12. Whichofthefo1.1.owingdoesnotstoremu1.tip1.ee1.ementscontiguous1.y?1.ist,deque,vector,String(Iist)13. void*inCis?(nu1.1.pointer/pointertonothing?)源地址:
