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1、SirIsaacNewtonandQuantitativeFinanceAsfarastheearthlyexperienceisconcerned,whatgoesupmustcomedown,andwhenevertheword“gravity”ismentioned,thename“Newton’’usuallyturnsup.WhatdoesNewtonhavetodowithQuantitativeFinance?WhatonearthisQuantitativeFinanceinthefirstplace?Toanswerthe
2、sequestions,wefirsttakealookattheplotofatimeseriesofstockpricesbelow:10.710.610.510.410.310.210.1109.99.89.7050100150200250Thepriceclimbsover$10.6after150tradingdaysbeforedescendingto$9.7overthenext50days.Itappearstohavebreachedthe“supportlevel”at$10.1onitswaydown,asifbein
3、gpulledbygravity.Whichstockisthis?Notanyrealone!These``prices’’wereinfactgeneratedbyacomputerprogramusingamathematicalmodelandastatisticalnumbergenerator.Thereyouhaveit.Computerprogramming,mathematicalmodeling,statistics,andahugedoseofcleverideaswithwhichtoexaminethephenom
4、enainthefinancialmarkets,arewhatQuantitativeFinanceisabout.Asdemonstratedintheabovefigure,QuantitativeFinancecanprovideratherrealisticsimulationofstockprices.Whatismore,therearethreebasicprinciplesinQuantitativeFinance.HereiswhereNewton,theauthorof“MathematicalPrinciplesof
5、NaturalPhilosophy"comesintothepicture.Inthismasterpieceofscience,Newtoninscribedtherenownedthreelawsofmotion.Theselawsgovernhowthemoonorbitsaroundtheearth,andpavethewayformankindtoimprint“smallsteps”onit282yearsafterthePrincipiawasfirstpublished.Standingonthegiantshoulders
6、ofNewton,thethreeprinciplesofQuantitativeFinancecanbestatedinparalleltoNewton’sthreelawsofmotion.Page1of4FirstLaw“Everybodyperseveresinitsstateofrestorofuniformmotioninarightlineunlessitiscompelledtochangethatstatebyforcesimpresseduponit,”Newtonwrites.Inotherwords,theveloc
7、ityofabodyremainsconstantunlessthebodyisacteduponbyanexternalforce.Thislawassertstheexistenceofaframeofreferenceinspacebywhichaphysicalbodyisobservedtobeeitherstationaryormovinginastraightlineatconstantspeed.NowinQuantitativeFinance,therisk-freeassetisonefinancialinstrumen
8、tforwhichthefuturecashflowisguaranteedandexactlypredictabletoday.Thereisabsolutelynouncer
