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PythonforFinance
YvesHilpisch
Beijing•Cambridge•Farnham•Köln•Sebastopol•Tokyo

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Preface
Nottoolongago,Pythonasaprogramminglanguageandplatformtechnologywas
consideredexotic—ifnotcompletelyirrelevant—inthefinancialindustry.Bycontrast,
in2014therearemanyexamplesoflargefinancialinstitutions—likeBankofAmerica
MerrillLynchwithitsQuartzproject,orJPMorganChasewiththeAthenaproject—that
strategicallyusePythonalongsideotherestablishedtechnologiestobuild,enhance,and
maintainsomeoftheircoreITsystems.Thereisalsoamultitudeoflargerandsmaller
hedgefundsthatmakeheavyuseofPython’scapabilitieswhenitcomestoefficient
financialapplicationdevelopmentandproductivefinancialanalyticsefforts.
Similarly,manyoftoday’sMasterofFinancialEngineeringprograms(orprograms
awardingsimilardegrees)usePythonasoneofthecorelanguagesforteachingthe
translationofquantitativefinancetheoryintoexecutablecomputercode.Educational
programsandtrainingstargetedtofinanceprofessionalsarealsoincreasingly
incorporatingPythonintotheircurricula.Somenowteachitasthemainimplementation
language.
TherearemanyreasonswhyPythonhashadsuchrecentsuccessandwhyitseemsitwill
continuetodosointhefuture.Amongthesereasonsareitssyntax,theecosystemof
scientificanddataanalyticslibrariesavailabletodevelopersusingPython,itseaseof
integrationwithalmostanyothertechnology,anditsstatusasopensource.(SeeChapter1
forafewmoreinsightsinthisregard.)
Forthatreason,thereisanabundanceofgoodbooksavailablethatteachPythonfrom

differentanglesandwithdifferentfocuses.Thisbookisoneofthefirsttointroduceand
teachPythonforfinance—inparticular,forquantitativefinanceandforfinancial
analytics.Theapproachisapracticalone,inthatimplementationandillustrationcome
beforetheoreticaldetails,andthebigpictureisgenerallymorefocusedonthanthemost
arcaneparameterizationoptionsofacertainclassorfunction.
Mostofthisbookhasbeenwritteninthepowerful,interactive,browser-basedIPython
Notebookenvironment(explainedinmoredetailinChapter2).Thismakesitpossibleto
providethereaderwithexecutable,interactiveversionsofalmostallexamplesusedinthis
book.
Thosewhowanttoimmediatelygetstartedwithafull-fledged,interactivefinancial
analyticsenvironmentforPython(and,forinstance,RandJulia)shouldgoto
andtryoutthePythonQuantPlatform(incombination
withtheIPythonNotebookfilesandcodethatcomewiththisbook).Youshouldalso
havealookatDXanalytics,aPython-basedfinancialanalyticslibrary.Myotherbook,
DerivativesAnalyticswithPython(WileyFinance),presentsmoredetailsonthetheory
andnumericalmethodsforadvancedderivativesanalytics.Italsoprovidesawealthof
readilyusablePythoncode.Furthermaterial,and,inparticular,slidedecksandvideosof
talksaboutPythonforQuantFinancecanbefoundonmyprivatewebsite.
IfyouwanttogetinvolvedinPythonforQuantFinancecommunityevents,thereare
opportunitiesinthefinancialcentersoftheworld.Forexample,Imyself(co)organize
meetupgroupswiththisfocusinLondon(cf. />

Finance-London/)andNewYorkCity(cf.TherearealsoForPythonQuantsconferencesandworkshopsseveral
timesayear(cf.and).
IamreallyexcitedthatPythonhasestablisheditselfasanimportanttechnologyinthe
financialindustry.Iamalsosurethatitwillplayanevenmoreimportantrolethereinthe
future,infieldslikederivativesandriskanalyticsorhighperformancecomputing.My
hopeisthatthisbookwillhelpprofessionals,researchers,andstudentsalikemakethe
mostofPythonwhenfacingthechallengesofthisfascinatingfield.


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ConventionsUsedinThisBook
Thefollowingtypographicalconventionsareusedinthisbook:
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Usedforprogramlistings,aswellaswithinparagraphstorefertosoftwarepackages,
programminglanguages,fileextensions,filenames,programelementssuchas
variableorfunctionnames,databases,datatypes,environmentvariables,statements,
andkeywords.
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Showstextthatshouldbereplacedwithuser-suppliedvaluesorbyvaluesdetermined
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TIP
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WARNING
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UsingCodeExamples
Supplementalmaterial(inparticular,IPythonNotebooksandPythonscripts/modules)is
availablefordownloadat.
Thisbookisheretohelpyougetyourjobdone.Ingeneral,ifexamplecodeisoffered

withthisbook,youmayuseitinyourprogramsanddocumentation.Youdonotneedto
contactusforpermissionunlessyou’rereproducingasignificantportionofthecode.For
example,writingaprogramthatusesseveralchunksofcodefromthisbookdoesnot
requirepermission.SellingordistributingaCD-ROMofexamplesfromO’Reillybooks
doesrequirepermission.Answeringaquestionbycitingthisbookandquotingexample
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fromthisbookintoyourproduct’sdocumentationdoesrequirepermission.
Weappreciate,butdonotrequire,attribution.Anattributionusuallyincludesthetitle,
author,publisher,andISBN.Forexample:“PythonforFinancebyYvesHilpisch
(O’Reilly).Copyright2015YvesHilpisch,978-1-491-94528-5.”
Ifyoufeelyouruseofcodeexamplesfallsoutsidefairuseorthepermissiongivenabove,
feelfreetocontactusat

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Acknowledgments
Iwanttothankallthosewhohelpedtomakethisbookareality,inparticularthosewho
haveprovidedhonestfeedbackorevencompletelyworkedoutexamples,likeBenLerner,
JamesPowell,MichaelSchwed,ThomasWieckiorFelixZumstein.Similarly,Iwould
liketothankreviewersHughBrown,JenniferPierce,KevinSheppard,andGalen

Wilkerson.Thebookbenefitedfromtheirvaluablefeedbackandthemanysuggestions.
ThebookhasalsobenefitedsignificantlyasaresultoffeedbackIreceivedfromthe
participantsofthemanyconferencesandworkshopsIwasabletopresentatin2013and
2014:PyData,ForPythonQuants,BigDatainQuantFinance,EuroPython,EuroScipy,
PyConDE,PyConIreland,ParallelDataAnalysis,BudapestBIForumandCodeJam.I
alsogotvaluablefeedbackduringmymanypresentationsatPythonmeetupsinBerlin,
London,andNewYorkCity.
Lastbutnotleast,Iwanttothankmyfamily,whichfullyacceptsthatIdowhatIlove
doingmostandthis,ingeneral,ratherintensively.Writingandfinishingabookofthis
lengthoverthecourseofayearrequiresalargetimecommitment—ontopofmyusually
heavyworkloadandpackedtravelschedule—andmakesitnecessarytositsometimes
morehoursinsolitudeinfrontthecomputerthanexpected.Therefore,thankyouSandra,
Lilli,andHenryforyourunderstandingandsupport.Idedicatethisbooktomylovely
wifeSandra,whoistheheartofourfamily.
YvesSaarland,November2014

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PartI.PythonandFinance
ThispartintroducesPythonforfinance.Itconsistsofthreechapters:

Chapter1brieflydiscussesPythoningeneralandargueswhyPythonisindeedwell
suitedtoaddressthetechnologicalchallengesinthefinanceindustryandinfinancial
(data)analytics.
Chapter2,onPythoninfrastructureandtools,ismeanttoprovideaconciseoverview
ofthemostimportantthingsyouhavetoknowtogetstartedwithinteractive
analyticsandapplicationdevelopmentinPython;therelatedAppendixAsurveys
someselectedbestpracticesforPythondevelopment.
Chapter3immediatelydivesintothreespecificfinancialexamples;itillustrateshow

tocalculateimpliedvolatilitiesofoptionswithPython,howtosimulateafinancial
modelwithPythonandthearraylibraryNumPy,andhowtoimplementabacktesting
foratrend-basedinvestmentstrategy.Thischaptershouldgivethereaderafeeling
forwhatitmeanstousePythonforfinancialanalytics—detailsarenotthat
importantatthisstage;theyareallexplainedinPartII.

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Chapter1.WhyPythonforFinance?
Banksareessentiallytechnologyfirms.
—HugoBanziger

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WhatIsPython?
Pythonisahigh-level,multipurposeprogramminglanguagethatisusedinawiderangeof
domainsandtechnicalfields.OnthePythonwebsiteyoufindthefollowingexecutive

summary(cf. />Python is an interpreted, object-oriented, high-level programming language with dynamic semantics. Its highlevel built in data structures, combined with dynamic typing and dynamic binding, make it very attractive for
RapidApplicationDevelopment,aswellasforuseasascriptingorgluelanguagetoconnectexistingcomponents
together.Python’ssimple,easytolearnsyntaxemphasizesreadabilityandthereforereducesthecostofprogram
maintenance.Pythonsupportsmodulesandpackages,whichencouragesprogrammodularityandcodereuse.The
Pythoninterpreterandtheextensivestandardlibraryareavailableinsourceorbinaryformwithoutchargeforall
majorplatforms,andcanbefreelydistributed.

ThisprettywelldescribeswhyPythonhasevolvedintooneofthemajorprogramming
languagesasoftoday.Nowadays,Pythonisusedbythebeginnerprogrammeraswellas
bythehighlyskilledexpertdeveloper,atschools,inuniversities,atwebcompanies,in

largecorporationsandfinancialinstitutions,aswellasinanyscientificfield.
Amongothers,Pythonischaracterizedbythefollowingfeatures:
Opensource
Pythonandthemajorityofsupportinglibrariesandtoolsavailableareopensource

andgenerallycomewithquiteflexibleandopenlicenses.
Interpreted
ThereferenceCPythonimplementationisaninterpreterofthelanguagethat
translatesPythoncodeatruntimetoexecutablebytecode.
Multiparadigm
Pythonsupportsdifferentprogrammingandimplementationparadigms,suchas

objectorientationandimperative,functional,orproceduralprogramming.
Multipurpose
Pythoncanbeusedforrapid,interactivecodedevelopmentaswellasforbuilding

largeapplications;itcanbeusedforlow-levelsystemsoperationsaswellasforhighlevelanalyticstasks.
Cross-platform
Pythonisavailableforthemostimportantoperatingsystems,suchasWindows,
Linux,andMacOS;itisusedtobuilddesktopaswellaswebapplications;itcanbe

usedonthelargestclustersandmostpowerfulserversaswellasonsuchsmall
devicesastheRaspberryPi(cf.).
Dynamicallytyped
TypesinPythonareingeneralinferredduringruntimeandnotstaticallydeclaredas
inmostcompiledlanguages.
Indentationaware
Incontrasttothemajorityofotherprogramminglanguages,Pythonusesindentation
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formarkingcodeblocksinsteadofparentheses,brackets,orsemicolons.
Garbagecollecting
Pythonhasautomatedgarbagecollection,avoidingtheneedfortheprogrammerto

managememory.
WhenitcomestoPythonsyntaxandwhatPythonisallabout,PythonEnhancement
Proposal20—i.e.,theso-called“ZenofPython”—providesthemajorguidelines.Itcan
beaccessedfromeveryinteractiveshellwiththecommandimportthis:
$ipython
Python2.7.6|Anaconda1.9.1(x86_64)|(default,Jan102014,11:23:15)
Type“copyright”,“credits”or“license”formoreinformation.
IPython2.0.0—AnenhancedInteractivePython.
?->IntroductionandoverviewofIPython’sfeatures.
%quickref->Quickreference.
help->Python’sownhelpsystem.
object?->Detailsabout‘object’,use‘object??’forextradetails.
In[1]:importthis
TheZenofPython,byTimPeters
Beautifulisbetterthanugly.
Explicitisbetterthanimplicit.
Simpleisbetterthancomplex.
Complexisbetterthancomplicated.
Flatisbetterthannested.
Sparseisbetterthandense.
Readabilitycounts.
Specialcasesaren’tspecialenoughtobreaktherules.
Althoughpracticalitybeatspurity.
Errorsshouldneverpasssilently.
Unlessexplicitlysilenced.

Inthefaceofambiguity,refusethetemptationtoguess.
Thereshouldbeone—andpreferablyonlyone—obviouswaytodoit.
Althoughthatwaymaynotbeobviousatfirstunlessyou’reDutch.
Nowisbetterthannever.
Althoughneverisoftenbetterthan*right*now.
Iftheimplementationishardtoexplain,it’sabadidea.
Iftheimplementationiseasytoexplain,itmaybeagoodidea.
Namespacesareonehonkinggreatidea—let’sdomoreofthose!

BriefHistoryofPython
AlthoughPythonmightstillhavetheappealofsomethingnewtosomepeople,ithasbeen
aroundforquitealongtime.Infact,developmenteffortsbeganinthe1980sbyGuidovan
RossumfromtheNetherlands.HeisstillactiveinPythondevelopmentandhasbeen
awardedthetitleofBenevolentDictatorforLifebythePythoncommunity(cf.
Thefollowingcanbeconsidered
milestonesinthedevelopmentofPython:

Python0.9.0releasedin1991(firstrelease)
Python1.0releasedin1994
Python2.0releasedin2000
Python2.6releasedin2008
Python2.7releasedin2010
Python3.0releasedin2008
Python3.3releasedin2010
Python3.4releasedin2014

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Itisremarkable,andsometimesconfusingtoPythonnewcomers,thattherearetwomajor

versionsavailable,stillbeingdevelopedand,moreimportantly,inparallelusesince2008.
Asofthiswriting,thiswillkeeponforquiteawhilesinceneitheristhere100%code
compatibilitybetweentheversions,norareallpopularlibrariesavailableforPython3.x.
ThemajorityofcodeavailableandinproductionisstillPython2.6/2.7,andthisbookis
basedonthe2.7.xversion,althoughthemajorityofcodeexamplesshouldworkwith
versions3.xaswell.

ThePythonEcosystem
AmajorfeatureofPythonasanecosystem,comparedtojustbeingaprogramming
language,istheavailabilityofalargenumberoflibrariesandtools.Theselibrariesand
toolsgenerallyhavetobeimportedwhenneeded(e.g.,aplottinglibrary)orhavetobe
startedasaseparatesystemprocess(e.g.,aPythondevelopmentenvironment).Importing
meansmakingalibraryavailabletothecurrentnamespaceandthecurrentPython
interpreterprocess.
Pythonitselfalreadycomeswithalargesetoflibrariesthatenhancethebasicinterpreter

indifferentdirections.Forexample,basicmathematicalcalculationscanbedonewithout
anyimporting,whilemorecomplexmathematicalfunctionsneedtobeimportedthrough
themathlibrary:
In[2]:100*2.5+50
Out[2]:300.0
In[3]:log(1)
…
NameError:name‘log’isnotdefined
In[4]:frommathimport*
In[5]:log(1)
Out[5]:0.0

Althoughtheso-called“starimport”(i.e.,thepracticeofimportingeverythingfroma
libraryviafromlibraryimport*)issometimesconvenient,oneshouldgenerallyuse

analternativeapproachthatavoidsambiguitywithregardtonamespacesand
relationshipsoffunctionstolibraries.Thisthentakesontheform:
In[6]:importmath
In[7]:math.log(1)
Out[7]:0.0

WhilemathisastandardPythonlibraryavailablewithanyinstallation,therearemany
morelibrariesthatcanbeinstalledoptionallyandthatcanbeusedintheverysame
fashionasthestandardlibraries.Suchlibrariesareavailablefromdifferent(web)sources.
However,itisgenerallyadvisabletouseaPythondistributionthatmakessurethatall
librariesareconsistentwitheachother(seeChapter2formoreonthistopic).
ThecodeexamplespresentedsofaralluseIPython(cf.),whichis
probablythemostpopularinteractivedevelopmentenvironment(IDE)forPython.
Althoughitstartedoutasanenhancedshellonly,ittodayhasmanyfeaturestypically
foundinIDEs(e.g.,supportforprofilinganddebugging).Thosefeaturesmissingare
typicallyprovidedbyadvancedtext/codeeditors,likeSublimeText(cf.
).Therefore,itisnotunusualtocombineIPythonwithone’s
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text/codeeditorofchoicetoformthebasictoolsetforaPythondevelopmentprocess.
IPythonisalsosometimescalledthekillerapplicationofthePythonecosystem.It

enhancesthestandardinteractiveshellinmanyways.Forexample,itprovidesimproved
command-linehistoryfunctionsandallowsforeasyobjectinspection.Forinstance,the
helptextforafunctionisprintedbyjustaddinga?behindthefunctionname(adding??
willprovideevenmoreinformation):
In[8]:math.log?
Type:builtin_function_or_method
StringForm:<built-infunctionlog>

Docstring:
log(x[,base])
Returnthelogarithmofxtothegivenbase.
Ifthebasenotspecified,returnsthenaturallogarithm(basee)ofx.
In[9]:

IPythoncomesinthreedifferentversions:ashellversion,onebasedonaQTgraphical
userinterface(theQTconsole),andabrowser-basedversion(theNotebook).Thisisjust

meantasateaser;thereisnoneedtoworryaboutthedetailsnowsinceChapter2
introducesIPythoninmoredetail.

PythonUserSpectrum
Pythondoesnotonlyappealtoprofessionalsoftwaredevelopers;itisalsoofuseforthe

casualdeveloperaswellasfordomainexpertsandscientificdevelopers.
Professionalsoftwaredevelopersfindallthattheyneedtoefficientlybuildlarge
applications.Almostallprogrammingparadigmsaresupported;therearepowerful
developmenttoolsavailable;andanytaskcan,inprinciple,beaddressedwithPython.
Thesetypesofuserstypicallybuildtheirownframeworksandclasses,alsoworkonthe
fundamentalPythonandscientificstack,andstrivetomakethemostoftheecosystem.
Scientificdevelopersordomainexpertsaregenerallyheavyusersofcertainlibrariesand
frameworks,havebuilttheirownapplicationsthattheyenhanceandoptimizeovertime,
andtailortheecosystemtotheirspecificneeds.Thesegroupsofusersalsogenerally
engageinlongerinteractivesessions,rapidlyprototypingnewcodeaswellasexploring
andvisualizingtheirresearchand/ordomaindatasets.
CasualprogrammersliketousePythongenerallyforspecificproblemstheyknowthat
Pythonhasitsstrengthsin.Forexample,visitingthegallerypageofmatplotlib,copying
acertainpieceofvisualizationcodeprovidedthere,andadjustingthecodetotheirspecific
needsmightbeabeneficialusecaseformembersofthisgroup.

ThereisalsoanotherimportantgroupofPythonusers:beginnerprogrammers,i.e.,those
thatarejuststartingtoprogram.Nowadays,Pythonhasbecomeaverypopularlanguage
atuniversities,colleges,andevenschoolstointroducestudentstoprogramming.[1]A
majorreasonforthisisthatitsbasicsyntaxiseasytolearnandeasytounderstand,even
forthenondeveloper.Inaddition,itishelpfulthatPythonsupportsalmostall
programmingstyles.[2]

TheScientificStack
Thereisacertainsetoflibrariesthatiscollectivelylabeledthescientificstack.Thisstack
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comprises,amongothers,thefollowinglibraries:
NumPy
NumPyprovidesamultidimensionalarrayobjecttostorehomogenousor

heterogeneousdata;italsoprovidesoptimizedfunctions/methodstooperateonthis
arrayobject.
SciPy
SciPyisacollectionofsublibrariesandfunctionsimplementingimportantstandard

functionalityoftenneededinscienceorfinance;forexample,youwillfindfunctions
forcubicsplinesinterpolationaswellasfornumericalintegration.
matplotlib

ThisisthemostpopularplottingandvisualizationlibraryforPython,providingboth
2Dand3Dvisualizationcapabilities.
PyTables
PyTablesisapopularwrapperfortheHDF5datastoragelibrary(cf.


itisalibrarytoimplementoptimized,disk-based
I/Ooperationsbasedonahierarchicaldatabase/fileformat.
pandas
pandasbuildsonNumPyandprovidesricherclassesforthemanagementandanalysis
oftimeseriesandtabulardata;itistightlyintegratedwithmatplotlibforplotting
andPyTablesfordatastorageandretrieval.

Dependingonthespecificdomainorproblem,thisstackisenlargedbyadditional
libraries,whichmoreoftenthannothaveincommonthattheybuildontopofoneormore
ofthesefundamentallibraries.However,theleastcommondenominatororbasicbuilding
blockingeneralistheNumPyndarrayclass(cf.Chapter4).
TakingPythonasaprogramminglanguagealone,thereareanumberofotherlanguages
availablethatcanprobablykeepupwithitssyntaxandelegance.Forexample,Rubyis
quiteapopularlanguageoftencomparedtoPython.Onthelanguage’swebsiteyoufind
thefollowingdescription:
A dynamic, open source programming language with a focus on simplicity and productivity. It has an elegant
syntaxthatisnaturaltoreadandeasytowrite.

ThemajorityofpeopleusingPythonwouldprobablyalsoagreewiththeexactsame
statementbeingmadeaboutPythonitself.However,whatdistinguishesPythonformany
usersfromequallyappealinglanguageslikeRubyistheavailabilityofthescientificstack.
ThismakesPythonnotonlyagoodandelegantlanguagetouse,butalsoonethatis
capableofreplacingdomain-specificlanguagesandtoolsetslikeMatlaborR.Inaddition,
itprovidesbydefaultanythingthatyouwouldexpect,say,asaseasonedwebdeveloperor
systemsadministrator.

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TechnologyinFinance

NowthatwehavesomeroughideasofwhatPythonisallabout,itmakessensetostep
backabitandtobrieflycontemplatetheroleoftechnologyinfinance.Thiswillputusin
apositiontobetterjudgetherolePythonalreadyplaysand,evenmoreimportantly,will
probablyplayinthefinancialindustryofthefuture.
Inasense,technologyperseisnothingspecialtofinancialinstitutions(ascompared,for
instance,toindustrialcompanies)ortothefinancefunction(ascomparedtoother
corporatefunctions,likelogistics).However,inrecentyears,spurredbyinnovationand
alsoregulation,banksandotherfinancialinstitutionslikehedgefundshaveevolvedmore
andmoreintotechnologycompaniesinsteadofbeingjustfinancialintermediaries.
Technologyhasbecomeamajorassetforalmostanyfinancialinstitutionaroundthe
globe,havingthepotentialtoleadtocompetitiveadvantagesaswellasdisadvantages.
Somebackgroundinformationcanshedlightonthereasonsforthisdevelopment.

TechnologySpending
Banksandfinancialinstitutionstogetherformtheindustrythatspendsthemoston
technologyonanannualbasis.Thefollowingstatementthereforeshowsnotonlythat
technologyisimportantforthefinancialindustry,butthatthefinancialindustryisalso
reallyimportanttothetechnologysector:
Bankswillspend4.2%moreontechnologyin2014thantheydidin2013,accordingtoIDCanalysts.OverallIT
spend in financial services globally will exceed $430 billion in 2014 and surpass $500 billion by 2020, the
analystssay.
—Crosman2013

Large,multinationalbankstodaygenerallyemploythousandsofdevelopersthatmaintain
existingsystemsandbuildnewones.Largeinvestmentbankswithheavytechnological
requirementsshowtechnologybudgetsoftenofseveralbillionUSDperyear.

TechnologyasEnabler
Thetechnologicaldevelopmenthasalsocontributedtoinnovationsandefficiency
improvementsinthefinancialsector:

Technologicalinnovationshavecontributedsignificantlytogreaterefficiencyinthederivativesmarket.Through
innovationsintradingtechnology,tradesatEurexaretodayexecutedmuchfasterthantenyearsagodespitethe
strong increase in trading volume and the number of quotes … These strong improvements have only been
possibleduetotheconstant,highITinvestmentsbyderivativesexchangesandclearinghouses.
—DeutscheBörseGroup2008

Asasideeffectoftheincreasingefficiency,competitiveadvantagesmustoftenbelooked
forinevermorecomplexproductsortransactions.Thisinturninherentlyincreasesrisks
andmakesriskmanagementaswellasoversightandregulationmoreandmoredifficult.
Thefinancialcrisisof2007and2008tellsthestoryofpotentialdangersresultingfrom
suchdevelopments.Inasimilarvein,“algorithmsandcomputersgonewild”also
representapotentialrisktothefinancialmarkets;thismaterializeddramaticallyinthesocalledflashcrashofMay2010,whereautomatedsellingledtolargeintradaydropsin
certainstocksandstockindices(cf. />
TechnologyandTalentasBarrierstoEntry
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Ontheonehand,technologyadvancesreducecostovertime,ceterisparibus.Ontheother
hand,financialinstitutionscontinuetoinvestheavilyintechnologytobothgainmarket
shareanddefendtheircurrentpositions.Tobeactiveincertainareasinfinancetoday
oftenbringswithittheneedforlarge-scaleinvestmentsinbothtechnologyandskilled
staff.Asanexample,considerthederivativesanalyticsspace(seealsothecasestudyin
PartIIIofthebook):
Aggregatedoverthetotalsoftwarelifecycle,firmsadoptingin-housestrategiesforOTC[derivatives]pricingwill
require investments between $25 million and $36 million alone to build, maintain, and enhance a complete
derivativeslibrary.
—Ding2010

Notonlyisitcostlyandtime-consumingtobuildafull-fledgedderivativesanalytics
library,butyoualsoneedtohaveenoughexpertstodoso.Andtheseexpertshavetohave

therighttoolsandtechnologiesavailabletoaccomplishtheirtasks.
AnotherquoteabouttheearlydaysofLong-TermCapitalManagement(LTCM),formerly
oneofthemostrespectedquantitativehedgefunds—which,however,wentbustinthe
late1990s—furthersupportsthisinsightabouttechnologyandtalent:
Meriwetherspent$20milliononastate-of-the-artcomputersystemandhiredacrackteamoffinancialengineers
toruntheshowatLTCM,whichsetupshopinGreenwich,Connecticut.Itwasriskmanagementonanindustrial
level.
—Patterson2010

ThesamecomputingpowerthatMeriwetherhadtobuyformillionsofdollarsistoday
probablyavailableforthousands.Ontheotherhand,trading,pricing,andrisk
managementhavebecomesocomplexforlargerfinancialinstitutionsthattodaytheyneed
todeployITinfrastructureswithtensofthousandsofcomputingcores.

Ever-IncreasingSpeeds,Frequencies,DataVolumes
Thereisonedimensionofthefinanceindustrythathasbeeninfluencedmostby
technologicaladvances:thespeedandfrequencywithwhichfinancialtransactionsare
decidedandexecuted.TherecentbookbyLewis(2014)describesso-calledflashtrading
—i.e.,tradingatthehighestspeedspossible—invividdetail.
Ontheonehand,increasingdataavailabilityonever-smallerscalesmakesitnecessaryto
reactinrealtime.Ontheotherhand,theincreasingspeedandfrequencyoftradingletthe
datavolumesfurtherincrease.Thisleadstoprocessesthatreinforceeachotherandpush
theaveragetimescaleforfinancialtransactionssystematicallydown:
Renaissance’s Medallion fund gained an astonishing 80 percent in 2008, capitalizing on the market’s extreme
volatility with its lightning-fast computers. Jim Simons was the hedge fund world’s top earner for the year,
pocketingacool$2.5billion.
—Patterson2010

Thirtyyears’worthofdailystockpricedataforasinglestockrepresentsroughly7,500
quotes.Thiskindofdataiswhatmostoftoday’sfinancetheoryisbasedon.Forexample,

theorieslikethemodernportfoliotheory(MPT),thecapitalassetpricingmodel(CAPM),
andvalue-at-risk(VaR)allhavetheirfoundationsindailystockpricedata.
Incomparison,onatypicaltradingdaythestockpriceofAppleInc.(AAPL)isquoted
around15,000times—twotimesasmanyquotesasseenforend-of-dayquotingovera

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timespanof30years.Thisbringswithitanumberofchallenges:
Dataprocessing
Itdoesnotsufficetoconsiderandprocessend-of-dayquotesforstocksorother
financialinstruments;“toomuch”happensduringthedayforsomeinstruments
during24hoursfor7daysaweek.
Analyticsspeed
Decisionsoftenhavetobemadeinmillisecondsorevenfaster,makingitnecessary
tobuildtherespectiveanalyticscapabilitiesandtoanalyzelargeamountsofdatain
realtime.
Theoreticalfoundations
Althoughtraditionalfinancetheoriesandconceptsarefarfrombeingperfect,they
havebeenwelltested(andsometimeswellrejected)overtime;forthemillisecond
scalesimportantasoftoday,consistentconceptsandtheoriesthathaveproventobe
somewhatrobustovertimearestillmissing.
Allthesechallengescaninprincipleonlybeaddressedbymoderntechnology.Something
thatmightalsobealittlebitsurprisingisthatthelackofconsistenttheoriesoftenis
addressedbytechnologicalapproaches,inthathigh-speedalgorithmsexploitmarket
microstructureelements(e.g.,orderflow,bid-askspreads)ratherthanrelyingonsome
kindoffinancialreasoning.

TheRiseofReal-TimeAnalytics
Thereisonedisciplinethathasseenastrongincreaseinimportanceinthefinance

industry:financialanddataanalytics.Thisphenomenonhasacloserelationshiptothe
insightthatspeeds,frequencies,anddatavolumesincreaseatarapidpaceintheindustry.
Infact,real-timeanalyticscanbeconsideredtheindustry’sanswertothistrend.
Roughlyspeaking,“financialanddataanalytics”referstothedisciplineofapplying
softwareandtechnologyincombinationwith(possiblyadvanced)algorithmsandmethods
togather,process,andanalyzedatainordertogaininsights,tomakedecisions,orto
fulfillregulatoryrequirements,forinstance.Examplesmightincludetheestimationof
salesimpactsinducedbyachangeinthepricingstructureforafinancialproductinthe
retailbranchofabank.Anotherexamplemightbethelarge-scaleovernightcalculationof
creditvalueadjustments(CVA)forcomplexportfoliosofderivativestradesofan
investmentbank.
Therearetwomajorchallengesthatfinancialinstitutionsfaceinthiscontext:
Bigdata
Banksandotherfinancialinstitutionshadtodealwithmassiveamountsofdataeven
beforetheterm“bigdata”wascoined;however,theamountofdatathathastobe
processedduringsingleanalyticstaskshasincreasedtremendouslyovertime,
demandingbothincreasedcomputingpowerandever-largermemoryandstorage
capacities.
Real-timeeconomy
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Inthepast,decisionmakerscouldrelyonstructured,regularplanning,decision,and
(risk)managementprocesses,whereastheytodayfacetheneedtotakecareofthese
functionsinrealtime;severaltasksthathavebeentakencareofinthepastvia
overnightbatchrunsinthebackofficehavenowbeenmovedtothefrontofficeand
areexecutedinrealtime.
Again,onecanobserveaninterplaybetweenadvancesintechnologyand
financial/businesspractice.Ontheonehand,thereistheneedtoconstantlyimprove
analyticsapproachesintermsofspeedandcapabilitybyapplyingmoderntechnologies.

Ontheotherhand,advancesonthetechnologysideallownewanalyticsapproachesthat
wereconsideredimpossible(orinfeasibleduetobudgetconstraints)acoupleofyearsor
evenmonthsago.
Onemajortrendintheanalyticsspacehasbeentheutilizationofparallelarchitectureson
theCPU(centralprocessingunit)sideandmassivelyparallelarchitecturesontheGPGPU
(general-purposegraphicalprocessingunits)side.CurrentGPGPUsoftenhavemorethan
1,000computingcores,makingnecessaryasometimesradicalrethinkingofwhat
parallelismmightmeantodifferentalgorithms.Whatisstillanobstacleinthisregardis
thatusersgenerallyhavetolearnnewparadigmsandtechniquestoharnessthepowerof
suchhardware.[3]

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PythonforFinance
Theprevioussectiondescribessomeselectedaspectscharacterizingtheroleoftechnology
infinance:

Costsfortechnologyinthefinanceindustry
Technologyasanenablerfornewbusinessandinnovation
Technologyandtalentasbarrierstoentryinthefinanceindustry
Increasingspeeds,frequencies,anddatavolumes
Theriseofreal-timeanalytics
Inthissection,wewanttoanalyzehowPythoncanhelpinaddressingseveralofthe
challengesimpliedbytheseaspects.Butfirst,onamorefundamentallevel,letusexamine
Pythonforfinancefromalanguageandsyntaxstandpoint.

FinanceandPythonSyntax
MostpeoplewhomaketheirfirststepswithPythoninafinancecontextmayattackan
algorithmicproblem.Thisissimilartoascientistwho,forexample,wantstosolvea

differentialequation,wantstoevaluateanintegral,orsimplywantstovisualizesomedata.
Ingeneral,atthisstage,thereisonlylittlethoughtspentontopicslikeaformal
developmentprocess,testing,documentation,ordeployment.However,thisespecially
seemstobethestagewhenpeoplefallinlovewithPython.Amajorreasonforthismight
bethatthePythonsyntaxisgenerallyquiteclosetothemathematicalsyntaxusedto
describescientificproblemsorfinancialalgorithms.
Wecanillustratethisphenomenonbyasimplefinancialalgorithm,namelythevaluation
ofaEuropeancalloptionbyMonteCarlosimulation.WewillconsideraBlack-ScholesMerton(BSM)setup(seealsoChapter3)inwhichtheoption’sunderlyingriskfactor
followsageometricBrownianmotion.
Supposewehavethefollowingnumericalparametervaluesforthevaluation:

InitialstockindexlevelS0=100
StrikepriceoftheEuropeancalloptionK=105
Time-to-maturityT=1year
Constant,risklessshortrater=5%
Constantvolatility=20%
IntheBSMmodel,theindexlevelatmaturityisarandomvariable,givenbyEquation1-1
withzbeingastandardnormallydistributedrandomvariable.
Equation1-1.Black-Scholes-Merton(1973)indexlevelatmaturity

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ThefollowingisanalgorithmicdescriptionoftheMonteCarlovaluationprocedure:

1. DrawI(pseudo)randomnumbersz(i),i∈{1,2,…,I},fromthestandardnormal
distribution.
2. CalculateallresultingindexlevelsatmaturityST(i)forgivenz(i)andEquation1-1.
3. CalculateallinnervaluesoftheoptionatmaturityashT(i)=max(ST(i)–K,0).
4. EstimatetheoptionpresentvalueviatheMonteCarloestimatorgiveninEquation12.

Equation1-2.MonteCarloestimatorforEuropeanoption

WearenowgoingtotranslatethisproblemandalgorithmintoPythoncode.Thereader
mightfollowthesinglestepsbyusing,forexample,IPython—thisis,however,not
reallynecessaryatthisstage.
First,letusstartwiththeparametervalues.Thisisreallyeasy:
S0=100.
K=105.
T=1.0
r=0.05
sigma=0.2

Next,thevaluationalgorithm.Here,wewillforthefirsttimeuseNumPy,whichmakeslife
quiteeasyforoursecondtask:
fromnumpyimport*
I=100000
z=random.standard_normal(I)
ST=S0*exp((r-0.5*sigma**2)*T+sigma*sqrt(T)*z)
hT=maximum(ST-K,0)
C0=exp(-r*T)*sum(hT)/I

Third,weprinttheresult:
print“ValueoftheEuropeanCallOption%5.3f”%C0

Theoutputmightbe:[4]
ValueoftheEuropeanCallOption8.019

Threeaspectsareworthhighlighting:
Syntax
ThePythonsyntaxisindeedquiteclosetothemathematicalsyntax,e.g.,whenit

comestotheparametervalueassignments.
Translation
Everymathematicaland/oralgorithmicstatementcangenerallybetranslatedintoa
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singlelineofPythoncode.
Vectorization
OneofthestrengthsofNumPyisthecompact,vectorizedsyntax,e.g.,allowingfor
100,000calculationswithinasinglelineofcode.
ThiscodecanbeusedinaninteractiveenvironmentlikeIPython.However,codethatis
meanttobereusedregularlytypicallygetsorganizedinso-calledmodules(orscripts),
whicharesinglePython(i.e.,text)fileswiththesuffix.py.Suchamodulecouldinthis
caselooklikeExample1-1andcouldbesavedasafilenamedbsm_mcs_euro.py.
Example1-1.MonteCarlovaluationofEuropeancalloption
#
#MonteCarlovaluationofEuropeancalloption
#inBlack-Scholes-Mertonmodel
#bsm_mcs_euro.py
#
importnumpyasnp
#ParameterValues
S0=100.#initialindexlevel
K=105.#strikeprice
T=1.0#time-to-maturity
r=0.05#risklessshortrate
sigma=0.2#volatility
I=100000#numberofsimulations
#ValuationAlgorithm
z=np.random.standard_normal(I)#pseudorandomnumbers

ST=S0*np.exp((r-0.5*sigma**2)*T+sigma*np.sqrt(T)*z)
#indexvaluesatmaturity
hT=np.maximum(ST-K,0)#innervaluesatmaturity
C0=np.exp(-r*T)*np.sum(hT)/I#MonteCarloestimator
#ResultOutput
print“ValueoftheEuropeanCallOption%5.3f”%C0

TherathersimplealgorithmicexampleinthissubsectionillustratesthatPython,withits
verysyntax,iswellsuitedtocomplementtheclassicduoofscientificlanguages,English
andMathematics.ItseemsthataddingPythontothesetofscientificlanguagesmakesit
morewellrounded.Wehave

Englishforwriting,talkingaboutscientificandfinancialproblems,etc.
Mathematicsforconciselyandexactlydescribingandmodelingabstractaspects,
algorithms,complexquantities,etc.
Pythonfortechnicallymodelingandimplementingabstractaspects,algorithms,
complexquantities,etc.
MATHEMATICSANDPYTHONSYNTAX
ThereishardlyanyprogramminglanguagethatcomesasclosetomathematicalsyntaxasPython.Numerical
algorithmsarethereforesimpletotranslatefromthemathematicalrepresentationintothePythonic
implementation.Thismakesprototyping,development,andcodemaintenanceinsuchareasquiteefficientwith
Python.

Insomeareas,itiscommonpracticetousepseudocodeandtherewithtointroducea
fourthlanguagefamilymember.Theroleofpseudocodeistorepresent,forexample,
financialalgorithmsinamoretechnicalfashionthatisbothstillclosetothemathematical

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representationandalreadyquiteclosetothetechnicalimplementation.Inadditiontothe
algorithmitself,pseudocodetakesintoaccounthowcomputersworkinprinciple.
Thispracticegenerallyhasitscauseinthefactthatwithmostprogramminglanguagesthe
technicalimplementationisquite“faraway”fromitsformal,mathematicalrepresentation.
Themajorityofprogramminglanguagesmakeitnecessarytoincludesomanyelements
thatareonlytechnicallyrequiredthatitishardtoseetheequivalencebetweenthe
mathematicsandthecode.
Nowadays,Pythonisoftenusedinapseudocodewaysinceitssyntaxisalmostanalogous
tothemathematicsandsincethetechnical“overhead”iskepttoaminimum.Thisis
accomplishedbyanumberofhigh-levelconceptsembodiedinthelanguagethatnotonly
havetheiradvantagesbutalsocomeingeneralwithrisksand/orothercosts.However,itis
safetosaythatwithPythonyoucan,whenevertheneedarises,followthesamestrict
implementationandcodingpracticesthatotherlanguagesmightrequirefromtheoutset.In
thatsense,Pythoncanprovidethebestofbothworlds:high-levelabstractionandrigorous
implementation.

EfficiencyandProductivityThroughPython
Atahighlevel,benefitsfromusingPythoncanbemeasuredinthreedimensions:
Efficiency
HowcanPythonhelpingettingresultsfaster,insavingcosts,andinsavingtime?
Productivity
HowcanPythonhelpingettingmoredonewiththesameresources(people,assets,
etc.)?
Quality
WhatdoesPythonallowustodothatwecouldnotdowithalternativetechnologies?
Adiscussionoftheseaspectscanbynaturenotbeexhaustive.However,itcanhighlight
someargumentsasastartingpoint.
Shortertime-to-results
AfieldwheretheefficiencyofPythonbecomesquiteobviousisinteractivedataanalytics.
ThisisafieldthatbenefitsstronglyfromsuchpowerfultoolsasIPythonandlibrarieslike

pandas.
Considerafinancestudent,writinghermaster’sthesisandinterestedinGooglestock
prices.Shewantstoanalyzehistoricalstockpriceinformationfor,say,fiveyearstosee
howthevolatilityofthestockpricehasfluctuatedovertime.Shewantstofindevidence
thatvolatility,incontrasttosometypicalmodelassumptions,fluctuatesovertimeandis
farfrombeingconstant.Theresultsshouldalsobevisualized.Shemainlyhastodothe
following:

DownloadGooglestockpricedatafromtheWeb.
Calculatetherollingstandarddeviationofthelogreturns(volatility).
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Plotthestockpricedataandtheresults.
Thesetasksarecomplexenoughthatnottoolongagoonewouldhaveconsideredthemto
besomethingforprofessionalfinancialanalysts.Today,eventhefinancestudentcan
easilycopewithsuchproblems.Letusseehowexactlythisworks—withoutworrying
aboutsyntaxdetailsatthisstage(everythingisexplainedindetailinsubsequentchapters).
First,makesuretohaveavailableallnecessarylibraries:
In[1]:importnumpyasnp
importpandasaspd
importpandas.io.dataasweb

Second,retrievethedatafrom,say,Googleitself:
In[2]:goog=web.DataReader(‘GOOG’,data_source=‘google’,
start=‘3/14/2009’,end=‘4/14/2014’)
goog.tail()
Out[2]:OpenHighLowCloseVolume
Date
2014-04-08542.60555.00541.61554.903152406

2014-04-09559.62565.37552.95564.143324742
2014-04-10565.00565.00539.90540.954027743
2014-04-11532.55540.00526.53530.603916171
2014-04-14538.25544.10529.56532.522568020
5rows×5columns

Third,implementthenecessaryanalyticsforthevolatilities:
In[3]:goog[‘Log_Ret’]=np.log(goog[‘Close’]/goog[‘Close’].shift(1))
goog[‘Volatility’]=pd.rolling_std(goog[‘Log_Ret’],
window=252)*np.sqrt(252)

Fourth,plottheresults.Togenerateaninlineplot,weusetheIPythonmagiccommand
%matplotlibwiththeoptioninline:
In[4]:%matplotlibinline
goog[[‘Close’,‘Volatility’]].plot(subplots=True,color=‘blue’,
figsize=(8,6))

Figure1-1showsthegraphicalresultofthisbriefinteractivesessionwithIPython.Itcan
beconsideredalmostamazingthatfourlinesofcodesufficetoimplementthreerather
complextaskstypicallyencounteredinfinancialanalytics:datagathering,complexand
repeatedmathematicalcalculations,andvisualizationofresults.Thisexampleillustrates
thatpandasmakesworkingwithwholetimeseriesalmostassimpleasdoing
mathematicaloperationsonfloating-pointnumbers.

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