Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

351 Pages·2013·6.45 MB·English

by  Alain Ruttiens

Mathematics of Financial Markets
ForothertitlesintheWileyFinanceseries
pleaseseewww.wiley.com/finance
Mathematics of Financial Markets
Financial Instruments and Derivatives Modeling,
Valuation and Risk Issues
Alain Ruttiens
A John Wiley & Sons, Ltd., Publication
Thiseditionfirstpublished2013
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Contents
ForewordbyA.G.MALLIARIS,LoyolaUniversity,Chicago xi
MainNotations xiii
Introduction xv
PARTI THEDETERMINISTICENVIRONMENT
1 PriortotheYieldCurve:SpotandForwardRates 3
1.1 InterestRates,PresentandFutureValues,InterestCompounding 3
1.2 DiscountFactors 5
1.3 ContinuousCompoundingandContinuousRates 6
1.4 ForwardRates 8
1.5 TheNoArbitrageCondition 11
FurtherReading 12
2 TheTermStructureorYieldCurve 13
2.1 IntroductiontotheYieldCurve 13
2.2 TheYieldCurveComponents 15
2.3 BuildingaYieldCurve:Methodology 17
2.4 AnExampleofYieldCurvePointsDetermination 21
2.5 InterpolationsonaYieldCurve 21
FurtherReading 22
3 SpotInstruments 23
3.1 Short-TermRates 23
3.2 Bonds 24
3.3 Currencies 43
FurtherReading 45
4 EquitiesandStockIndexes 47
4.1 StocksValuation 47
4.2 StockIndexes 51
viii Contents
4.3 ThePortfolioTheory 52
FurtherReading 73
5 ForwardInstruments 75
5.1 TheForwardForeignExchange 75
5.2 FRAs 84
5.3 OtherForwardContracts 86
5.4 ContractsforDifference(CFD) 88
FurtherReading 89
6 Swaps 91
6.1 DefinitionsandFirstExamples 91
6.2 PriortoanIRSSwapPricingMethod 94
6.3 PricingofanIRSSwap 99
6.4 (Re)ValuationofanIRSSwap 102
6.5 TheSwap(Rates)Market 103
6.6 PricingofaCRSSwap 105
6.7 PricingofSecond-GenerationSwaps 108
FurtherReading 118
7 Futures 119
7.1 IntroductiontoFutures 119
7.2 FuturesPricing 123
7.3 FuturesonEquitiesandStockIndexes 127
7.4 FuturesonShort-TermInterestRates 130
7.5 FuturesonBonds 132
7.6 FuturesonCurrencies 138
7.7 Futureson(Non-Financial)Commodities 139
FurtherReading 144
PARTII THEPROBABILISTICENVIRONMENT
8 TheBasisofStochasticCalculus 147
8.1 StochasticProcesses 147
8.2 TheStandardWienerProcess,orBrownianMotion 150
8.3 TheGeneralWienerProcess 152
8.4 TheItoˆ Process 152
8.5 ApplicationoftheGeneralWienerProcess 153
8.6 TheItoˆ Lemma 155
8.7 ApplicationoftheItoˆ Lemma 156
8.8 NotionofRiskNeutralProbability 158
8.9 NotionofMartingale 159
Annex8.1: ProofsofthePropertiesofdZ(t) 161
Annex8.2: ProofoftheItoˆ Lemma 163
FurtherReading 164