Financial Modelling in Python (The Wiley Finance Series)

246 Pages·2009·3.71 MB·English

by  Shayne Fletcher

Financial Modelling in Python
ForothertitlesintheWileyFinanceSeries
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Financial Modelling in Python
S. Fletcher & C. Gardner
A John Wiley and Sons, Ltd., Publication
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LibraryofCongressCataloging-in-PublicationData
Fletcher,Shayne.
FinancialmodelinginPython/ShayneFletcherandChristopherGardner.
p.cm.—(Wileyfinanc series)
Includesbibliographicalreferencesandindex.
ISBN978-0-470-98784-1(cloth:alk.paper) 1.Finance—Mathematicalmodels—Computerprograms.
2.Python(Computerprogramlanguage) I.Gardner,Christopher. II.Title.
HG106.F592009
(cid:2)
332.02855133—dc22
2009019336
ISBN 978-0-470-98784-1
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Typesetin10/12ptTimesbyAptaraInc.,NewDelhi,India
PrintedinGreatBritainbyAntonyRoweLtd,Chippenham,Wiltshire
Contents
1 WelcometoPython 1
1.1 WhyPython? 1
1.1.1 Pythonisageneral-purposehigh-levelprogramminglanguage 1
1.1.2 Pythonintegrateswellwithdataanalysis,visualisationand
GUItoolkits 2
1.1.3 Python‘playswellwithothers’ 2
1.2 CommonmisconceptionsaboutPython 2
1.3 Roadmapforthisbook 3
2 ThePPFPackage 5
2.1 PPFtopology 5
2.2 Unittesting 6
2.2.1 doctest 6
2.2.2 PyUnit 7
2.3 BuildingandinstallingPPF 7
2.3.1 Prerequisitesanddependencies 7
2.3.2 BuildingtheC++extensionmodules 8
2.3.3 InstallingthePPFpackage 9
2.3.4 TestingaPPFinstallation 9
3 ExtendingPythonfromC++ 11
3.1 Boost.Date Timetypes 11
3.1.1 Examples 12
3.2 Boost.MultiArrayandspecialfunctions 17
3.3 NumPyarrays 19
3.3.1 AccessingarraydatainC++ 19
3.3.2 Examples 23
4 BasicMathematicalTools 27
4.1 Randomnumbergeneration 27
4.2 N(.) 28
4.3 Interpolation 29
4.3.1 Linearinterpolation 31
vi Contents
4.3.2 Loglinearinterpolation 32
4.3.3 Linearonzerointerpolation 32
4.3.4 Cubicsplineinterpolation 33
4.4 Rootfindin 35
4.4.1 Bisectionmethod 35
4.4.2 Newton–Raphsonmethod 36
4.5 Linearalgebra 38
4.5.1 Matrixmultiplication 38
4.5.2 Matrixinversion 38
4.5.3 Matrixpseudo-inverse 39
4.5.4 Solvinglinearsystems 39
4.5.5 Solvingtridiagonalsystems 39
4.5.6 Solvingupperdiagonalsystems 40
4.5.7 Singularvaluedecomposition 42
4.6 Generalisedlinearleastsquares 44
4.7 Quadraticandcubicroots 46
4.8 Integration 49
4.8.1 Piecewiseconstantpolynomialfittin 49
4.8.2 Piecewisepolynomialintegration 51
4.8.3 Semi-analyticconditionalexpectations 57
5 Market:CurvesandSurfaces 63
5.1 Curves 63
5.2 Surfaces 64
5.3 Environment 65
6 DataModel 69
6.1 Observables 69
6.1.1 LIBOR 70
6.1.2 Swaprate 74
6.2 Flows 79
6.3 Adjuvants 82
6.4 Legs 84
6.5 Exercises 85
6.6 Trades 87
6.7 Tradeutilities 88
7 Timeline:EventsandController 93
7.1 Events 93
7.2 Timeline 94
7.3 Controller 97
8 TheHull–WhiteModel 99
8.1 Acomponent-baseddesign 99
8.1.1 Requestor 100
8.1.2 State 101
8.1.3 Filler 104
Contents vii
8.1.4 Rollback 108
8.1.5 Evolve 112
8.1.6 Exercise 115
8.2 Themodelandmodelfactories 118
8.3 Concludingremarks 121
9 PricingusingNumericalMethods 123
9.1 Alatticepricingframework 123
9.2 AMonte-Carlopricingframework 128
9.2.1 Pricingnon-callabletrades 129
9.2.2 Pricingcallabletrades 131
9.3 Concludingremarks 142
10 PricingFinancialStructuresinHull–White 145
10.1 PricingaBermudan 145
10.2 PricingaTARN 152
10.3 Concludingremarks 157
11 HybridPython/C++PricingSystems 159
11.1 nth imm of yearrevisited 159
11.2 Exercisingnth imm of yearfromC++ 161
12 PythonExcelIntegration 165
12.1 Black–scholesCOMserver 165
12.1.1 VBSclient 167
12.1.2 VBAclient 167
12.2 NumericalpricingwithPPFinExcel 168
12.2.1 Commonutilities 168
12.2.2 Marketserver 169
12.2.3 Tradeserver 176
12.2.4 Pricerserver 187
Appendices 191
A Python 193
A.1 Pythoninterpretermodes 193
A.1.1 Interactivemode 193
A.1.2 Batchmode 193
A.2 BasicPython 194
A.2.1 Simpleexpressions 194
A.2.2 Built-indatatypes 195
A.2.3 Controlfl wstatements 197
A.2.4 Functions 200
A.2.5 Classes 201
A.2.6 Modulesandpackages 203
A.3 Conclusion 205
viii Contents
B Boost.Python 207
B.1 Helloworld 207
B.2 Classes,constructorsandmethods 207
B.3 Inheritance 209
B.4 Pythonoperators 212
B.5 Functions 212
B.6 Enums 214
B.7 Embedding 214
B.8 Conclusion 216
C Hull–WhiteModelMathematics 217
D PickupValueRegression 219
Bibliography 221
Index 223