c# pdf library github : Add metadata to pdf file SDK software service wpf windows azure dnn Wiley%20Advanced%20Modelling%20in%20Finance%20using%20Excel%20and%20VBA0-part579

Advanced Modelling in Finance
using Excel and VBA
Mary Jackson
and
Mike Staunton
JOHNWILEY & SONS, LTD
Chichester
ž
NewYork
ž
Weinheim
ž
Brisbane
ž
Singapore
ž
Toronto
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Copyright2001byJohnWiley&Sons,Ltd,
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WestSussexPO191UD,England
National
01243779777
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Contents
Preface
xi
Acknowledgements
xii
1 Introduction
1
1.1
Finance insights
1
1.2
Assetprice assumptions
2
1.3
Mathematicaland statistical problems
2
1.4
Numericalmethods
2
1.5
Excel solutions
3
1.6
Topics covered
3
1.7
RelatedExcel workbooks
5
1.8
Comments andsuggestions
5
Part One Advanced Modelling in Excel
7
2 AdvancedExcelfunctions and procedures
9
2.1
Accessing functions inExcel
9
2.2
Mathematicalfunctions
10
2.3
Statisticalfunctions
12
2.3.1 Usingthefrequencyfunction
12
2.3.2 Usingthequartilefunction
14
2.3.3 UsingExcel’snormalfunctions
15
2.4
Lookupfunctions
16
2.5
Otherfunctions
18
2.6
Auditingtools
19
2.7
DataTables
20
2.7.1 SettingupDataTables withoneinput
20
2.7.2 SettingupDataTables withtwoinputs
22
2.8
XYcharts
23
2.9
Access toDataAnalysis andSolver
26
2.10 Usingrange names
27
2.11 Regression
28
2.12 GoalSeek
31
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vi
Contents
2.13 Matrixalgebra andrelatedfunctions
33
2.13.1 Introductiontomatrices
33
2.13.2 Transposinga matrix
33
2.13.3 Addingmatrices
34
2.13.4 Multiplying matrices
34
2.13.5 Matrix inversion
35
2.13.6 Solvingsystems of simultaneous linearequations
36
2.13.7 Summary ofExcel’s matrix functions
37
Summary
37
3 IntroductiontoVBA
39
3.1
Advantages ofmasteringVBA
39
3.2
Object-orientedaspects ofVBA
40
3.3
Startingtowrite VBAmacros
42
3.3.1
Some simple examples ofVBA subroutines
42
3.3.2
MsgBoxforinteraction
43
3.3.3
The writing environment
44
3.3.4
Entering code andexecutingmacros
44
3.3.5
Recordingkeystrokes andediting code
45
3.4
Elements ofprogramming
47
3.4.1
Variables anddata types
48
3.4.2
VBAarrayvariables
48
3.4.3
Controlstructures
50
3.4.4
Controlofrepeatingprocedures
51
3.4.5
UsingExcel functions andVBAfunctionsin code
52
3.4.6
Generalpoints on programming
53
3.5
Communicating between macrosand the spreadsheet
53
3.6
Subroutine examples
56
3.6.1
Charts
56
3.6.2
Normalprobabilityplot
59
3.6.3
GeneratingtheefficientfrontierwithSolver
61
Summary
65
References
65
Appendix 3A
The VisualBasic Editor
65
Steppingthrough amacroandusingother
debug tools
68
Appendix 3B Recordingkeystrokes in‘relativereferences’mode
69
4 WritingVBA user-definedfunctions
73
4.1
Asimple sales commissionfunction
73
4.2
Creating Commission(Sales)inthespreadsheet
74
4.3
Twofunctions with multiple inputs forvaluingoptions
75
4.4
Manipulatingarrays inVBA
78
4.5
Expected value and variancefunctions witharrayinputs
79
4.6
Portfoliovariance function with arrayinputs
81
4.7
Functions witharrayoutput
84
4.8
Using ExcelandVBAfunctions in user-definedfunctions
85
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Contents
vii
4.8.1 UsingVBAfunctions in user-definedfunctions
85
4.8.2 Add-ins
86
4.9
Pros andconsofdevelopingVBA functions
86
Summary
87
Appendix4AFunctions illustratingarrayhandling
88
Appendix4B Binomialtree optionvaluation functions
89
Exercises onwriting functions
94
Solution notes forexercises onfunctions
95
Part Two Equities
99
5 Introductiontoequities
101
6 Portfolio optimisation
103
6.1
Portfoliomeanandvariance
103
6.2
Risk–returnrepresentationofportfolios
105
6.3
UsingSolvertofindefficientpoints
106
6.4
Generatingtheefficientfrontier(HuangandLitzenberger’s
approach)
109
6.5
Constrainedfrontierportfolios
111
6.6
Combiningrisk-freeand riskyassets
113
6.7
ProblemOne–combining arisk-free asset witha riskyasset
114
6.8
ProblemTwo–combining two risky assets
115
6.9
ProblemThree–combining arisk-free asset witha riskyportfolio
117
6.10 User-definedfunctions inModule1
119
6.11 Functions forthe three genericportfolioproblems in Module1
120
6.12 Macrosin ModuleM
121
Summary
123
References
123
7 Assetpricing
125
7.1
The single-index model
125
7.2
Estimating beta coefficients
126
7.3
The capital asset pricing model
129
7.4
Variance–covariancematrices
130
7.5
Value-at-Risk
131
7.6
Horizonwealth
134
7.7
Moments ofrelated distributions such as normal andlognormal
136
7.8
User-definedfunctions inModule1
136
Summary
138
References
138
8 Performance measurementandattribution
139
8.1
Conventionalperformancemeasurement
140
8.2
Active–passivemanagement
141
8.3
Introduction tostyleanalysis
144
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viii
Contents
8.4
Simplestyle analysis
145
8.5
Rolling-period styleanalysis
146
8.6
Confidence intervals forstyle weights
148
8.7
User-definedfunctions inModule1
151
8.8
Macros in ModuleM
151
Summary
152
References
153
PartThree Options onEquities
155
9
Introductiontooptions onequities
157
9.1
The genesis ofthe Black–Scholesformula
158
9.2
The Black–Scholes formula
158
9.3
Hedgeportfolios
159
9.4
Risk-neutralvaluation
161
9.5
Asimple one-stepbinomialtreewith risk-neutralvaluation
162
9.6
Put–call parity
163
9.7
Dividends
163
9.8
Americanfeatures
164
9.9
Numericalmethods
164
9.10 Volatilityandnon-normalshare returns
165
Summary
165
References
166
10 Binomialtrees
167
10.1 Introductiontobinomialtrees
167
10.2 A simplified binomial tree
168
10.3 The Jarrowand Rudd binomial tree
170
10.4 The Cox, Ross and Rubinsteintree
173
10.5 Binomial approximations andBlack–Scholes formula
175
10.6 ConvergenceofCRR binomialtrees
176
10.7 The Leisen andReimertree
177
10.8 ComparisonofCRR andLRtrees
178
10.9 Americanoptions andthe CRRAmericantree
180
10.10 User-definedfunctions inModule0andModule1
182
Summary
183
References
184
11 The Black–Scholes formula
185
11.1 The Black–Scholes formula
185
11.2 Black–Scholes formula in the spreadsheet
186
11.3 Options oncurrenciesand commodities
187
11.4 Calculating the option’s ‘greek’parameters
189
11.5 Hedgeportfolios
190
11.6 Formalderivation ofthe Black–Scholes formula
192
Contents
ix
11.7 User-defined functions inModule1
194
Summary
195
References
196
12 Other numericalmethods for Europeanoptions
197
12.1 Introduction toMonte Carlo simulation
197
12.2 Simulationwithantitheticvariables
199
12.3 Simulationwithquasi-randomsampling
200
12.4 Comparing simulation methods
202
12.5 Calculatinggreeks inMonteCarlosimulation
203
12.6 Numericalintegration
203
12.7 User-defined functions inModule1
205
Summary
207
References
207
13 Non-normaldistributions andimpliedvolatility
209
13.1 Black–Scholes using alternative distributionalassumptions
209
13.2 Implied volatility
211
13.3 Adaptingforskewnessand kurtosis
212
13.4 The volatilitysmile
215
13.5 User-defined functions inModule1
217
Summary
219
References
220
Part Four Options on Bonds
221
14 Introductiontovaluing options onbonds
223
14.1 The termstructureofinterestrates
224
14.2 Cash flows forcoupon bonds andyield to maturity
225
14.3 Binomialtrees
226
14.4 Black’s bond optionvaluationformula
227
14.5 Durationandconvexity
228
14.6 Notation
230
Summary
230
References
230
15 Interestratemodels
231
15.1 Vasicek’s termstructuremodel
231
15.2 ValuingEuropean options onzero-couponbonds, Vasicek’s model
234
15.3 ValuingEuropean options oncouponbonds, Vasicek’s model
235
15.4 CIRtermstructure model
236
15.5 ValuingEuropean options onzero-couponbonds, CIR model
237
15.6 ValuingEuropean options oncouponbonds, CIR model
238
15.7 User-defined functions inModule1
239
Summary
240
References
241
x
Contents
16 Matchingtheterm structure
243
16.1 Treeswithlognormallydistributedinterest rates
243
16.2 Treeswithnormalinterestrates
246
16.3 The Black, DermanandToy tree
247
16.4 Valuingbondoptions using BDTtrees
248
16.5 User-definedfunctions inModule1
250
Summary
252
References
252
Appendix OtherVBA functions
253
Forecasting
253
ARIMA modelling
254
Splines
256
Eigenvalues andeigenvectors
257
References
258
Index
259
Preface
When asked whythey tackledMount Everest, climbers typically reply “Because it was
there”. Our motivation for writing Advanced Modelling in Finance is for exactly the
opposite reason. There were then, and still are now, almost no books that give due
prominence to and explanation of the use of VBA functions within Excel. There is an
almost similar lack of books that capture the true vibrant spirit of numerical methods
infinance.
Itis nolongertrue thatspreadsheetssuchas Excelare inadequate toolsinhighlytech-
nicalandnumericallydemandingareassuchasthevaluationoffinancialderivatives.With
efficientcode andVBA functions, calculations that were once the preserve ofdedicated
packages and languages can now be done on a modern PC in Excel within seconds, if
not fractions ofa second. By employing Excel andVBA, ourpurposeis to try to bring
clarity to anareathatwas previouslycovered withblackboxes.
WhatstartedasanattempttopushbacktheboundariesofExcelthroughmacrosturned
intoafull-scaleexpeditionintothe VBAlanguagewithinExcelandthendevelopedfrom
equities,throughoptionsandfinallytocoverbonds. Along the waywe learnedscoresof
newExcelskillsandamuchgreaterunderstandingofthenumericalmethodsimplemented
across finance.
Thegenesisofthebookcamefrommaterialdevelopedforthe‘Computer-BasedFinan-
cial Modelling’ elective on the MBA degree at London Business School. The part on
equities formedthebasis foranexecutive courseon‘EquityPortfolioManagement’run
annually by the International Centre for Money and Banking in Geneva. The parts on
options andbonds comprise acoursein ‘NumericalMethods’ontheMSc in Mathemat-
icalTradingandFinanceatCityUniversityBusinessSchool.Thebookiswithinthereach
ofbothstudents atthe postgraduate level andthoseinthe latterundergraduateyears.
There are no prerequisites for readers apart from a willingness to adopt a pro-active
stancewhenusingthebook–namelybytakingadvantageoftheinherent‘what-if’quality
ofthespreadsheets andbylooking atandusingthe code forming the VBAuser-defined
functions.Sinceweassumeforthemostpartthatassetreturnsarelognormalandtherefore
use binomial trees as a central numerical method, our explanations can be based on
familiarresults from probabilityand statistics. Comprehension is helpedby the use ofa
common notation throughout, andtransparency by theavailabilityofcomplete solutions
inbothExcel andVBAforms.
Acknowledgements
Our main debt is to the individuals fromthe academic and practitionercommunities in
finance who first developed the theory and then the numerical methods that form the
material for this book. In thewords of SirIsaac Newton“IfIhave seen further itis by
standingonthe shouldersofgiants”.
We wouldalso like tothank our colleaguesat both London Business SchoolandCity
UniversityBusiness School, inparticularElroyDimson, JohnHatgioannides, PaulMarsh
and Kiriakos Vlahos.
We would like to thank Sam Whittaker at Wiley for herenthusiasm, encouragement
and much needed patience, invaluablequalities foran editor.
Last but not least, we are grateful for the patience of family and friends who have
occasionallychivvied us aboutthebook’s somewhat lengthygestation period.
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