Interest Rate Derivatives Explained: Volume 1: Products and Markets

223 Pages·2015·6.364 MB·English

by  Jörg Kienitz

InterestRateDerivativesExplained
FinancialEngineeringExplained
Abouttheseries
FinancialEngineeringExplainedisaseriesofconcise,practicalguidestomodernfinance,focusingonkey,
technicalareasofriskmanagementandassetpricing. Writtenforpractitioners,researchersandstudents,
theseriesdiscussesarangeoftopicsinanon-mathematicalbuthighlyintuitiveway.Eachself-contained
volumeisdedicatedtoaspecifictopicandoffersathoroughintroductionwithallthenecessarydepth,but
withouttoomuchtechnicalballast.Whereapplicable,theoryisillustratedwithrealworldexamples,with
specialattentiontothenumericalimplementation.
SeriesEditor:
WimSchoutens,DepartmentofMathematics,CatholicUniversityofLeuven.
SeriesAdvisoryBoard:
PeterCarr,ExecutiveDirector,NYUMathematicalFinance;GlobalHeadofMarketModeling,
MorganStanley.
ErnstEberlein,DepartmentofMathematicalStochastics,UniversityofFreiburg.
MatthiasScherer,ChairofMathematicalFinance,TechnischeUniversitätMünchen.
Titlesintheseries:
EquityDerivativesExplained,MohamedBouzoubaa
TheGreeksandHedgingExplained,PeterLeoni
SmilePricingExplained,PeterAusting
FinancialEngineeringwithCopulasExplained,MatthiasSchererandJan-FrederikMai
InterestRateDerivativesExplainedVolume1,JörgKienitz
Forthcomingtitles:
InterestRateDerivativesExplainedVolume2,JörgKienitz
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FinancialEngineeringExplainedseries
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Interest Rate Derivatives
Explained
Volume 1: Products and Markets
Jörg Kienitz
©JörgKienitz2014
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ToAmberley,BeatriceandBenoît

vii
Contents
ListofFigures x
ListofTables xiii
Introduction GoalsofthisBookandGlobaloverview 1
I.1 Introductionandmanagementsummary 1
I.2 Shortoverview 2
I.3 Useofthebook 4
I.4 Credits 4
PartI MarketsandLinearProducts
1 Clearing,Collateral,Pricing 7
1.1 Introductionandobjectives 7
1.2 Nettingandcollateral 7
1.3 Clearing 10
1.3.1 Whatiscentralclearing? 10
1.3.2 Clearingmembers 13
1.3.3 Resume 14
1.4 Counterpartycreditrisk 14
1.5 Generalpricingtheory 17
1.5.1 Numeraire 22
1.6 Readinglist 22
2 Rates 24
2.1 Introductionandobjectives 24
2.2 Daycount,rollingandotherconventions 24
2.2.1 Daycount 25
2.3 Rates 27
2.3.1 Rollconventions–businessdates 28
2.3.2 Discountfactors 32
2.3.3 Forwardrates 32
2.3.4 Otherrates 33
2.3.5 Interestratecurves 33
2.4 Readinglist 34
3 MarketsandProducts–Deposits,Bonds,Futures,Repo 35
3.1 Introductionandobjectives 35
viii Contents
3.2 Deposits 35
3.2.1 Marketquotes 35
3.3 Futures 35
3.4 Bonds 37
3.4.1 Bondmath 38
3.4.2 Parrate 40
3.4.3 Yieldtomaturity 41
3.4.4 Bondriskmeasures 42
3.5 Repos 44
3.6 Marketquotes 47
3.7 Readinglist 47
4 MarketsandProducts–FRAsandSwaps 48
4.1 Introductionandobjectives 48
4.2 FRAs 48
4.2.1 FRAmath 49
4.2.2 FRAquotes 50
4.3 Swaps 50
4.3.1 Fixedagainstfloatinterestrateswap 51
4.3.2 Swapquotes 53
4.3.3 Inarrearsswaps 54
4.4 Floatagainstfloatinterestrateswaps 62
4.4.1 Moneymarketbasisswaps 62
4.4.2 Constantmaturityswaps(CMS) 65
4.4.3 Othertypeofswaps 65
4.5 Readinglist 69
5 UsingCurves 70
5.1 Introductionandobjectives 70
5.2 Interpolationmethods 70
5.2.1 Constantinterpolation 71
5.2.2 Linearinterpolation 71
5.2.3 Cubicsplineinterpolation 72
5.2.4 Whichmethodtouseandhow? 77
5.3 Curveconstruction 77
5.3.1 Bootstrapping 79
5.3.2 Curveconstruction–optimization 99
5.4 Riskmeasures 103
5.4.1 Riskmeasures1D 103
5.4.2 RiskmeasuresnD 105
5.4.3 Forwardbuckets 106
5.5 Interpolationintwoandthreedimensions 112
5.6 Example:capandfloorvolatilities 113
5.7 Readinglist 113
Contents ix
PartII MarketsandNon-LinearProducts
6 OptionsI 119
6.1 Introductionandobjectives 119
6.2 Marketconventions 119
6.2.1 Blackmodel 119
6.2.2 Normalmodel 120
6.2.3 Displaceddiffusionmodel–shiftedblackmodel 121
6.3 Capsandfloors 121
6.3.1 Cap/Floormath 122
6.3.2 Cap/Floorquotes 123
6.4 Swaptions 128
6.4.1 Swaptionmath 130
6.4.2 Swaptionquotes 132
6.4.3 Theswaptionsmile/skew 132
6.5 Transformingvolatility 133
6.5.1 Transformingcapletvolatilities 137
6.5.2 Transformingswaptionvolatilities 143
6.5.3 Examples 147
6.6 Bondoptions 148
6.7 Readinglist 151
7 OptionsII 152
7.1 Introductionandobjectives 152
7.2 CMScapsandfloors 153
7.2.1 CMSmath 155
7.2.2 CMSquotes 166
7.3 CMSspreadoptions 166
7.3.1 CMSspreadoptionmath 170
7.3.2 CMSspreadoptionquotes 182
7.4 Readinglist 182
PartIII CounterpartyCreditRiskAdjustments
8 Adjustments 189
8.1 Introductionandobjectives 189
8.2 Thecreditvalueadjustment(CVA) 189
8.3 BilateralCVA(BCVA)anddebitvalueadjustment(DVA) 193
8.4 Thefundingvalueadjustment(FVA) 194
8.5 CVA,DVA,FVA–whattodo? 195
8.5.1 Example 196
8.6 Readinglist 197
Bibliography 200
Index 204