04 Products and Strategies Lecture Notes

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1、Coverage•InterestRates•TimeValueofMoney•MoneyMarketSecurities•InterestRateSwaps•CurrencyMarkets•Bonds•Commodities•Equities•FuturesandFuturesPricing•OptionsandOptionPricingCertificateinQuantitativeFinance1TimeValueofMoneyCompoundingCompoundingistheeffectoflettingmoneyaccumulateovertimewithinterest

2、.Thecompoundingformulaisasfollows:•TV=PV(1+r)nWhereTVistheterminalvalueofanamountPVinvestedtodayfornperiodsataninterestrateofrperperiod.Example:Calculatetheterminalvalueof$20,000investedfor14yearsat5.16%p.a.$20,000x1.051614=$40,451.82CertificateinQuantitativeFinance2Non-annualCompoundingIntheform

3、ula,nisthenumberofperiodsandristheperiodicrate.Therelationshipbetweennandrmustalwaysbekeptconstant.Also,interestratesaregenerallyquotedasnominalannualrates.Thismeanswedividetheannualratebythefrequencyofthepayments:n´færö•FV=PV´çç1+÷÷èføWhereTVistheterminalvalueofanamountPVinvestedtodayfornperiods

4、ataninterestrateofrperperiodpaidatafrequencyofftimesperperiod.CertificateinQuantitativeFinance3Ifweincreasethefrequencywithwhichtheinterestispaidmoreinterestisearned.Noticehow,withincreasingfrequency,theextrainterestearneddiminishes:Example:Calculatetheterminalvalueof$100for1yearat5%p.a2æ0.05ö•Pa

5、idsemi-annually100ç1+÷=105.0625è2ø12•Paidmonthly100æ1+0.05ö÷=105.1162çè12ø365•Paiddaily100æ1+0.05ö÷=105.1267çè365ø8,760•Paidonceperhour(8,760times)æ0.05ö100ç1+÷=105.1271è8,760øCertificateinQuantitativeFinance4CONTINUOUSCOMPOUNDINGAstheinterestpaymentsperperiodareincreasedthefinalamountapproachesa

6、constantvalueof105.1271…Adirectmethodforcalculatingthefinalamountaftercontinuouscompoundingistousetheefunction,orexp()inExcel.Tocalculatetheterminalvalue(TV)withcontinuouscompoundingweusetheformula:TV=PVern•PVisthepresentvalueofanamountofmoneyinvestednow•eisaconstantwithavalueof2.71828•risthenomi

7、alinterestrateforoneperiod•nisthenumberofperiodsCertificateinQuantitativeFinance5ExampleWhatisthefinalvalueof$1,000paidfortwoyearsatarateof8%usingcontinuouslycompounding?0.08´2$1000e=$1,173.51InExcel:CertificateinQuant