Statistical Analysis of Financial Data in R PDF
Preview Statistical Analysis of Financial Data in R
Springer Texts in Statistics René Carmona Statistical Analysis of Financial Data in R Second Edition Springer Texts in Statistics SeriesEditors: G.Casella R.DeVeaux S.E.Fienberg I.Olkin Forfurthervolumes: http://www.springer.com/series/417 Rene´ Carmona Statistical Analysis of Financial Data in R Second Edition 123 Rene´Carmona DepartmentofOperationsResearch andFinancialEngineering PrincetonUniversity Princeton,NJ,USA ISSN1431-875X ISSN2197-4136(electronic) ISBN978-1-4614-8787-6 ISBN978-1-4614-8788-3(eBook) DOI10.1007/978-1-4614-8788-3 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2013951152 ©SpringerScience+BusinessMediaNewYork2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection withreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeingenteredand executedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplicationofthispub- licationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthePublisher’s location,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Permis- sionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violationsareliable toprosecutionundertherespectiveCopyrightLaw. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) To Chanel, Chelsea, and Ste´phanie Preface Like its earlier incarnation in S-Plus written over 10 years ago, this book is a polished version of the lecture notes written for a one-semester junior statistics courseofferedtotheundergraduatestudentsmajoringintheDepartmentofOpera- tionsResearchandFinancialEngineeringandacorecourseoftheMaster’sprogram oftheBendheimCenterforFinanceatPrincetonUniversity. Thecommongoalofbothcoursesistointroducestudentstomoderndataanal- ysis used in the financial industry. The prerequisites are minimal, though students areexpectedtohavealreadytakenabasicintroductorystatisticscourse.Elementary notionsofrandomvariables,expectation,andcorrelationaretakenforgranted,and earlierexposuretostatisticalinference(estimation,tests,andconfidenceintervals)is assumed.Itisalsoexpectedthatthestudentsarefamiliarwithaminimumoflinear algebraaswellasvectorandmatrixcalculus.However,allthebackgroundconcepts andresultsnecessaryforthecomprehensionofthematerialpresentedinthebook(as wellasthesolutionsofthehomeworkproblems)arerecalledbeforetheyareusedor needed. Bychoice,thecoursesarebothcomputationalandmathematicalinnature.Most problems considered are formulated in a rigorous manner. Mathematical facts are motivatedbyapplications,stated precisely,justifiedatan intuitivelevel,butessen- tially never proven rigorously.The emphasis is more on the relevance of concepts andonthepracticaluseoftools,ratherthanontheirtheoreticalunderpinnings. Ichosetoillustrateconcepts,manipulatedata,buildmodels,andimplementesti- mationandpredictionproceduresintheRcomputerenvironment.Forthisreasonthe textissprinkledwiththeRcommandsneededtoperformtheanalysesandproduce the plots. The first incarnation of this text was written for S-Plus on Windows platforms.ThegrowingpresenceofMaccomputersintheclassroomsandtheease with which Linux, Windows, and MacOS versionsof R can be downloadedand installedatnocostwereinfluentialinmydecisiontoswitchfromS-PlustoR.To vii viii PREFACE mysurprise,theportwasnotasseamlessasIoriginallyexpected.Ittookmeseveral years to complete the transition, and in the process, an entire chapter, several sec- tions,andalargenumberofexamplesandproblemshavebeenaddedtotheoriginal contents. The text is divided into three parts. Part I, Data Exploration, Estimation, and Simulation,introducesheavy tail distributionsand dependenceconceptsfor multi- variatedata,with an emphasisonthe practicalapplicationsof copulas.PartII, Re- gression,introducesthestudentstomodernregressionwithanemphasisonrobust- nessandnonparametrictechniques.PartIII,TimeSeriesandStateSpaceModels,is concernedwiththetheoriesoftimeseriesandstatespacemodels,includingfiltering applications. CONTENTS PartIcomprisesthreechapters.Chapter1beginswithareviewoftheclassicalprob- ability distributions encounteredthroughoutthe book and presents the exploratory dataanalysistechniques(histograms,kerneldensityestimators,Q-Qplots,etc.)used tohandleempiricalsamples.Asapreparationformanyanalysesandproblemsbased on random simulations, the chapter concludes with a discussion of Monte Carlo computations. Chapter 2 is devoted to the detection, estimation, and simulation of heavy tail distributionsalreadyshowcasedinthefirstchapter.Itcontainsmorestatementsand discussionsoftheoreticalresultsthanmostotherchapters,thereasonbeingthedesire to provide insight in the estimation and simulation algorithms implemented in the R library Rsafd used in the practical applications. Illustrative examples are used to demonstrate the impact of the presence of heavy tails on the computations of measuresofrisksuchasvalueatrisk(alsoknownasVaR). The third chapter is concerned with multivariate distributions and the various concepts of dependence. We review the classical measures of correlation, demon- strate the shortcomingsofthe Pearsoncorrelationcoefficient,and study the notion ofcopula,andtheimportantroleitplayswhenthemarginaldistributionshaveheavy tails, both in the bivariate case and in the high dimensionalcase. We learn how to detect unusual dependencies, estimate and simulate them, and bring this expertise to bearon the analysisof largeportfoliosof financialinstrumentsincludingstocks andcreditderivatives.Thechapterconcludeswithacompletediscussionofprincipal componentanalysisandtwoapplicationstothefixedincomemarkets. Part II is concerned with regression, and it is naturally divided into two chap- ters:thefirstdevotedtoparametricmethodsandthesecondtononparametricones. Chapter4dealswithlinearmodelsandtheirapplications.Thenotionofrobustnessis introduced,andexamplesareusedtoillustratethedifferencesbetweenleastsquares and least absolute deviations regressions. Applications of linear models include Preface ix polynomial and more general nonlinear regressions. We use financial examples throughout, and we analyze the term structure of interest rates in detail. Chap- ter5isconcernedwithnonparametricregression.Wecomparethepropertiesofdata smoothersforunivariatedata,andweanalyzeindetailthemultivariatekernelregres- sion.Forlargerdimensions,weuseprojectionpursuit.Examplesofenergyforward curvesandintradayS&P500futurestickdataaregiven.Thelastpartofthischapter isdevotedtotheuseofsemi-parametricandnonparametricmethodsinoptionpric- ing.Wedemonstratetheimplementationofmodernregressiontechniquesaspricing alternativestotheclassicalBlack-Scholespricingformula. ThefirstchapterofPartIIIisdevotedtotheclassicallinearmodelsfortimeseries andtotheidiosyncrasiesoftheRobjectsandmethodsincludedinthelibraryRsafd forthesolepurposeoftheiranalyses.Wediscussautoregressiveandmoving-average models,andwe give examplesof their use in practice.The mainapplicationis the analysis of temperature data. Even if it may not appear to be much of a financial application at first, we recast this analysis in the frameworkof financial risk man- agement via a thorough discussion of the market of weather derivatives. We give practicalexamplestoillustratetheuseofthestatisticaltechniquesintroducedinthis chaptertothecontrolofthesefinancialinstruments. Inthefollowingtwochapters,weturntotheanalysisofpartiallyobservedstate space systems. Chapter 7 deals with linear models and the classical Kalman filter. Forillustrationpurposes,we studytwo financialapplications,onerelatedtoanex- tension of the CAPM model and a second dealing with the analysis of quarterly companyearnings.Chapter8isdevotedtotheanalysisofnonlineartimeseries.We first consider the natural generalizations of the linear time series models, and we provideanextensivereviewofthetheoryandthepracticeofthefamousARCHand GARCH models. We also consider models from continuous time finance through theirdiscretizedforms.Aspecialsectionisdevotedtotheuseofscenariosforeco- nomic modeling. We concentrate on scenarios for a stock index and the short and long interest rates. These scenarios are of crucial importance in risk management wheretheyareusedasinputtolargestochasticoptimizationprograms.Finally,we revisitthetheorypresentedinthecaseofpartiallyobservedlinearsystems,andwe extendthefilteringparadigmtononlinearsystemswiththehelpofrecentadvances inMonteCarlotechniquesandtheso-calledparticlefilters.Wegiveseveralapplica- tionsofthismaterial,includingtheestimationofstochasticvolatilityandcommodity convenienceyield. Eachchaptercontainsaproblemsection.Mostpracticalproblemsarerootedin (cid:2) (cid:2) financialapplications.Eachproblemisprecededbyoneorseveralsymbols E , S, (cid:2) and/or T intended as hints suggesting if it is of an empirical, simulation, and/or theoreticalnature.ChaptersendwithNotesandComplementssectionsthatinclude complementsand bibliographicreferencesfor the readers interested in acquiringa deeperunderstandingofthetopicsofthatchapter.Thebookendswithanappendix andasuiteofindexes.Theappendixcontainsthetextofanintroductorysessionto RintendedtohelpthereaderunfamiliarwithRgetstartedandtoacrashcourseon Black-Scholesoptionpricingtheoryusedinseveralchapters.
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