Statistics of Financial Markets: Exercises and Solutions PDF
Preview Statistics of Financial Markets: Exercises and Solutions
Universitext Universitext SeriesEditors: SheldonAxler SanFranciscoStateUniversity VincenzoCapasso Universita` degliStudidiMilano CarlesCasacuberta UniversitatdeBarcelona AngusJ.MacIntyre QueenMary,UniversityofLondon KennethRibet UniversityofCalifornia,Berkeley ClaudeSabbah CNRS,E´colePolytechnique EndreSu¨li UniversityofOxford WojborA.Woyczynski CaseWesternReserveUniversity Universitextisaseriesoftextbooksthatpresentsmaterialfromawidevarietyof mathematicaldisciplinesatmaster’slevelandbeyond.Thebooks,oftenwell class-testedbytheirauthor,mayhaveaninformal,personalevenexperimental approachtotheirsubjectmatter.Someofthemostsuccessfulandestablished booksintheserieshaveevolvedthroughseveraleditions,alwaysfollowingthe evolutionofteachingcurricula,toverypolishedtexts. Thus as research topics trickle down into graduate-level teaching, first textbooks writtenfornew,cutting-edgecoursesmaymaketheirwayintoUniversitext. Forfurthervolumes: www.springer.com/series/223 Szymon Borak Wolfgang Karl Ha¨rdle (cid:2) Brenda Lo´pez-Cabrera Statistics of Financial Markets Exercises and Solutions Second Edition 123 SzymonBorak WolfgangKarlHa¨rdle BrendaLo´pez-Cabrera Humboldt-Universita¨tzuBerlin LadislausvonBortkiewiczChairofStatistics C.A.S.E.CentreforAppliedStatisticsandEconomics SchoolofBusinessandEconomics Berlin Germany Quantlets may be downloaded from http://extras.springer.com or via a link on http://springer.com/ 978-3-642-33928-8orwww.quantlet.orgforarepositoryofquantlets. ISBN978-3-642-33928-8 ISBN978-3-642-33929-5(eBook) DOI10.1007/978-3-642-33929-5 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2012954542 ©Springer-VerlagBerlinHeidelberg2010,2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface to the Second Edition Morepracticemakesyouevenmoreperfect.Manyreadersofthefirsteditionofthis book have followed this advice. We have received very helpful comments of the usersofourbookandwehavetriedtomakeitmoreperfectbypresentingyouthe secondeditionwithmorequantletsinMatlabandRandwithmoreexercises,e.g., forExoticOptions(Chap.9). This new edition is a good complement for the third edition of Statistics of FinancialMarkets.Ithascreatedmanyfinancialengineeringpractitionersfromthe poolof students at C.A.S.E. at Humboldt-Universita¨tzu Berlin. We would like to express our sincere thanks for the highly motivating comments and feedback on our quantlets. Very special thanks go to the Statistics of Financial Markets class of 2012 for their active collaboration with us. We would like to thank in partic- ular Mengmeng Guo, Shih-Kang Chao, Elena Silyakova, Zografia Anastasiadou, AnnaRamisch,MatthiasFengler,AlexanderRistig,AndreasGolle,JasminKrauß, AwdeschMelzer,GagandeepSinghand,lastbutnotleast,DerrickKanngießer. Berlin,Germany,January2013 SzymonBorak WolfgangKarlHa¨rdle BrendaLo´pezCabrera v • Preface to the First Edition WirbehaltenvonunserenStudienamEndedochnurdas,was wirpraktischanwenden. “Intheend,wereallyonlyretainfromourstudiesthatwhichwe applyinapracticalway.” J.W.Goethe,Gespra¨chemitEckermann,24.Feb.1824. The complexity of modern financial markets requires good comprehension of economic processes, which are understood through the formulation of statistical models.Nowadaysonecanhardlyimaginethesuccessfulperformanceoffinancial products without the support of quantitative methodology. Risk management, option pricing and portfolio optimisation are typical examples of extensive usage of mathematical and statistical modelling. Models simplify complex reality; the simplificationthoughmightstilldemandahighlevelofmathematicalfitness.One has to be familiar with the basic notionsof probability theory,stochastic calculus and statistical techniques. In addition,data analysis, numericaland computational skillsareamust. Practice makes perfect. Therefore the best method of mastering models is workingwiththem.Inthisbook,wepresentacollectionofexercisesandsolutions which can be helpful in the advanced comprehension of Statistics of Financial Markets. Our exercises are correlated to Franke, Ha¨rdle, and Hafner (2011). The exercisesillustratethetheorybydiscussingpracticalexamplesindetail.Weprovide computationalsolutions for the majority of the problems.All numericalsolutions arecalculatedwithRandMatlab.Thecorrespondingquantlets–anamewegiveto theseprogramcodes–areindicatedby inthetextofthisbook.Theyfollowthe nameschemeSFSxyz123andcanbedownloadedfromtheSpringerhomepageof thisbookorfromtheauthors’homepages. Financialmarketsareglobal.Wehavethereforeadded,beloweachchaptertitle, the corresponding translation in one of the world languages. We also head each section with a proverb in one of those world languages. We start with a German proverbfromGoetheontheimportanceofpractice. vii viii PrefacetotheFirstEdition We have tried to achieve a good balance between theoretical illustration and practicalchallenges.We havealsokeptthepresentationrelativelysmoothand,for more detailed discussion, refer to more advanced text books that are cited in the referencesections. Thebookisdividedintothreemainpartswherewediscusstheissuesrelatingto optionpricing,timeseriesanalysisandadvancedquantitativestatisticaltechniques. Themainmotivationforwritingthisbookcamefromourstudentsofthecourse Statistics of Financial Markets which we teach at the Humboldt-Universita¨t zu Berlin. The students expressed a strong demand for solving additional problems and assured us that (in line with Goethe) giving plenty of examples improves learningspeed and quality.We are gratefulfor their highly motivatingcomments, commitment and positive feedback. In particular we would like to thank Richard Song, Julius Mungo, Vinh Han Lien, Guo Xu, Vladimir Georgescu and Uwe ZiegenhagenforadviceandsolutionsonLaTeX.Wearegratefultoourcolleagues Ying Chen, Matthias Fengler and Michel Benko for their inspiring contributions to the preparation of lectures. We thank Niels Thomas from Springer-Verlag for continuoussupportandforvaluablesuggestionsonthewritingstyleandthecontent covered. Berlin,Germany SzymonBorak WolfgangHa¨rdle BrendaLo´pezCabrera Contents PartI OptionPricing 1 Derivatives................................................................... 3 2 IntroductiontoOptionManagement..................................... 13 3 BasicConceptsofProbabilityTheory.................................... 25 4 StochasticProcessesinDiscreteTime.................................... 35 5 StochasticIntegralsandDifferentialEquations ........................ 43 6 Black-ScholesOptionPricingModel..................................... 59 7 BinomialModelforEuropeanOptions .................................. 79 8 AmericanOptions.......................................................... 91 9 ExoticOptions .............................................................. 101 10 ModelsfortheInterestRateandInterestRateDerivatives ........... 119 PartII StatisticalModelofFinancialTimeSeries 11 FinancialTimeSeriesModels............................................. 131 12 ARIMATimeSeriesModels .............................................. 143 13 TimeSerieswithStochasticVolatility.................................... 163 PartIII SelectedFinancialApplications 14 ValueatRiskandBacktesting............................................. 177 15 CopulaeandValueatRisk................................................. 189 16 StatisticsofExtremeRisks ................................................ 197 ix
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