Contents
0 Goals of this Book and Global Overview 1
0.1 What is this book? 1
0.2 Why has this book been written? 1
0.3 For whom is this book intended? 2
0.4 Why should I read this book? 2
0.5 The structure of this book 2
0.6 What this book does not cover 2
0.7 More information and support 3
PART I C++ ESSENTIAL SKILLS 5
1 Introduction to C++ and Quantitative Finance 7
1.1 Introduction and objectives 7
1.2 A short history of C++ 7
1.3 C++, a multi-paradigm language 8
1.3.1 Object-oriented paradigm 8
1.3.2 Generic programming 10
1.3.3 Procedural, modular and functional programming 11
1.4 C++ and quantitative finance: what’s the relationship? 11
1.5 What is software quality? 11
1.6 Summary and conclusions 13
1.7 Exercises 14
2 The Mechanics of C++: from Source Code to a Running Program 15
2.1 Introduction and objectives 15
2.2 The compilation process 15
2.3 Header files and source files 16
2.4 Creating classes and using their objects 19
2.5 Template classes and template functions 22
2.6 Kinds of errors 25
2.6.1 Compiler errors 25
2.6.2 Linker errors 26
2.6.3 Run-time errors 26
2.7 The struct concept 27

2.8 Useful data conversion routines 27
2.9 Summary and conclusions 29
2.10 Exercises and projects 29
3 C++ Fundamentals and My First Option Class 31
3.1 Introduction and objectives 31
3.2 Class == member data + member functions 32
3.3 The header file (function prototypes) 33
3.4 The class body (code file) 35
3.5 Using the class 38
3.6 Examining the class in detail 40
3.6.1 Accessibility issues 40
3.6.2 Using standard libraries 40
3.6.3 The scope resolution operator ‘::’ 41
3.6.4 Virtual destructor: better safe than sorry 41
3.7 Other paradigms 41
3.8 Summary and conclusions 45
3.9 Questions, exercises and projects 45
4 Creating Robust Classes 49
4.1 Introduction and objectives 49
4.2 Call by reference and call by value 49
4.3 Constant objects everywhere 52
4.3.1 Read-only (const) member functions 52
4.4 Constructors in detail 54
4.4.1 Member initialisation 55
4.5 Static member data and static member functions 55
4.6 Function overloading 57
4.7 Non-member functions 58
4.8 Performance tips and guidelines 58
4.8.1 The ‘inline’ keyword 58
4.8.2 Anonymous objects in function code 59
4.8.3 Loop optimisation 60
4.9 Summary and conclusions 60
4.10 Questions, exercises and projects 60
5 Operator Overloading in C++ 63
5.1 Introduction and objectives 63
5.2 What is operator overloading and what are the possibilities? 63
5.3 Why use operator overloading? The advantages 65
5.4 Operator overloading: the steps 68
5.4.1 A special case: the assignment operator 70
5.5 Using operator overloading for simple I/O 71
5.6 Friend functions in general 72
5.6.1 Friend classes 73
5.7 Summary and conclusions 74
5.8 Exercise 74
Appendix: useful data structures in C++ 75

6 Memory Management in C++ 79
6.1 Introduction and objectives 79
6.2 Single objects and arrays of objects on the stack 79
6.3 Special operators: ‘new’ and ‘delete’ 82
6.3.1 Single objects 82
6.3.2 Arrays of objects 83
6.4 Small application: working with complex numbers 84
6.5 Creating an array class 86
6.5.1 Memory allocation and deallocation 86
6.5.2 Accessing functions 87
6.5.3 Examples 88
6.5.4 The full header file 88
6.6 Summary and conclusions 89
6.7 Exercises 89
6.8 Review questions and comments 91
7 Functions, Namespaces and Introduction to Inheritance 93
7.1 Introduction and objectives 93
7.2 Functions and function pointers 93
7.2.1 Functions in financial engineering 94
7.2.2 Function categories 94
7.2.3 Modelling functions in C++ 95
7.2.4 Application areas for function pointers, part I 96
7.3 An introduction to namespaces in C++ 96
7.3.1 Some extra functionality 97
7.4 An introduction to the inheritance mechanism in C++ 99
7.4.1 Basic inheritance structure 99
7.4.2 Adding new functionality 101
7.4.3 Overriding functionality: polymorphic and
non-polymorphic behaviour 102
7.5 Multiple inheritance 104
7.6 Solution of nonlinear equations 104
7.7 Nonlinear solvers in C++: design and implementation 106
7.8 Applying nonlinear solvers: calculating volatility 108
7.9 Summary and conclusions 109
7.10 Exercises and projects 109
8 Advanced Inheritance and Payoff Class Hierarchies 113
8.1 Introduction and objectives 113
8.2 The virtual specifier and memory deallocation 113
8.3 Abstract and concrete classes 115
8.3.1 Using payoff classes 118
8.4 Lightweight payoff classes 119
8.5 Super lightweight payoff functions 121
8.6 The dangers of inheritance: a counterexample 123
8.7 Implementation inheritance and fragile base class problem 127
8.7.1 Deep hierarchies 127
8.7.2 Multiple inheritance problems 127

8.8 Two-factor payoff functions and classes 127
8.9 Conclusions and summary 130
8.10 Exercises and projects 130
9 Run-Time Behaviour in C++ 133
9.1 Introduction and objectives 133
9.2 An introduction to reflection and self-aware objects 133
9.3 Run-time type information (RTTI) 134
9.4 Casting between types 137
9.4.1 More esoteric casting 139
9.5 Client-server programming and exception handling 140
9.6 try, throw and catch: ingredients of the C++ exception mechanism 141
9.7 C++ implementation 141
9.8 Pragmatic exception mechanisms 145
9.8.1 An example of use 148
9.9 Conclusions and summary 149
9.10 Exercises and research 149
10 An Introduction to C++ Templates 153
10.1 Introduction and objectives 153
10.2 My first template class 154
10.2.1 Using template classes 156
10.2.2 (Massive) reusability of the range template class 157
10.3 Template functions 158
10.4 Consolidation: understanding templates 159
10.4.1 A test program 162
10.5 Summary and conclusions 163
10.6 Exercises and projects 164
PART II DATA STRUCTURES, TEMPLATES AND PATTERNS 167
11 Introduction to Generic Data Structures and Standard
Template Library (STL) 169
11.1 Introduction and objectives 169
11.2 Complexity analysis 170
11.2.1 Examples of complexities 171
11.3 An introduction to data structures 172
11.3.1 Lists 172
11.3.2 Stacks and queues 173
11.3.3 Sets and multisets 174
11.3.4 Maps and multimaps 176
11.4 Algorithms 176
11.5 Navigation in data structures: iterators in STL 177
11.6 STL by example: my first example 178
11.6.1 Constructors and memory allocation 179
11.6.2 Iterators 179
11.6.3 Algorithms 179

11.7 Conclusions and summary 183
11.8 Exercises and projects 183
12 Creating Simpler Interfaces to STL for QF Applications 187
12.1 Introduction and objectives 187
12.2 Maps and dictionaries 187
12.2.1 Iterating in maps 188
12.2.2 Erasing records in a map 189
12.3 Applications of maps 190
12.4 User-friendly sets 191
12.4.1 STL sets 192
12.4.2 User-defined and wrapper classes for STL sets 194
12.5 Associative arrays and associative matrices 196
12.6 Applications of associative data structures 199
12.7 Conclusions and summary 200
12.8 Exercises and projects 200
13 Data Structures for Financial Engineering Applications 203
13.1 Introduction and objectives 203
13.2 The property pattern 203
13.3 Property sets 205
13.3.1 Basic functionality 206
13.3.2 Addition and removal of properties 207
13.3.3 Navigating in a property set: creating your own iterators 208
13.3.4 Property sets with heterogeneous data types 209
13.4 Property sets and data modelling for quantitative finance 213
13.4.1 Fixed assemblies (assemblies-parts relationship) 213
13.4.2 Collection-members relationship 213
13.4.3 Container-contents relationship 215
13.4.4 Recursive and nested property sets 215
13.5 Lattice structures 215
13.5.1 Some simple examples 217
13.5.2 A simple binomial method solver 219
13.6 Conclusions and summary 221
13.7 Exercises and projects 221
14 An Introduction to Design Patterns 223
14.1 Introduction and objectives 223
14.2 The software lifecycle 223
14.3 Documentation issues 225
14.3.1 Generalisation and specialisation 225
14.3.2 Aggregation and composition 227
14.3.3 Associations 229
14.3.4 Other diagrams 232
14.4 An Introduction to design patterns 233
14.4.1 Creational patterns 233
14.4.2 Structural patterns 236
14.4.3 Behavioural patterns 237

14.5 Are we using the wrong design? Choosing the appropriate pattern 237
14.6 CADObject, a C++ library for computer graphics 238
14.7 Using patterns in CADObject 240
14.8 Conclusions and summary 241
14.9 Exercises and projects 242
PART III QF APPLICATIONS 243
15 Programming the Binomial Method in C++ 245
15.1 Introduction and objectives 245
15.2 Scoping the problem 246
15.3 A short overview of the binomial method 246
15.4 Software requirements for a binomial solver 249
15.5 Class design and class structure 250
15.5.1 UML class structure 250
15.5.2 Information flow 251
15.6 Applying design patterns 252
15.7 The builder and director classes 255
15.8 The process and the steps 258
15.9 Test cases and examples 259
15.10 Conclusions and summary 260
15.11 Exercises and questions 260
16 Implementing One-Factor Black Scholes in C++ 265
16.1 Introduction and objectives 265
16.2 Scope and assumptions 265
16.3 Assembling the C++ building blocks 267
16.4 Modelling the black scholes PDE 267
16.4.1 Creating your own one-factor financial models 270
16.5 Finite difference schemes 270
16.5.1 Explicit schemes 272
16.5.2 Implicit schemes 273
16.5.3 A note on exception handling 275
16.5.4 Other schemes 275
16.6 Test cases and presentation in excel 276
16.6.1 Creating the user interface dialogue 276
16.6.2 Vector and matrix output 278
16.6.3 Presentation 278
16.7 Summary 279
16.8 Exercises and projects 279
17 Two-Factor Option Pricing: Basket and Other Multi-Asset Options 283
17.1 Introduction and objectives 283
17.2 Motivation and background 283
17.3 Scoping the problem: PDEs for basket options 285
17.4 Modelling basket option PDE in UML and C++ 286
17.4.1 Data classes for instruments 286
17.4.2 Modelling the PDE with C++ classes 292

17.5 The finite difference method for two-factor problems 297
17.6 Discrete boundary and initial conditions 298
17.7 Assembling the system of equations 299
17.8 Post processing and output 301
17.9 Summary and conclusions 302
17.10 Exercises and projects 302
18 Useful C++ Classes for Numerical Analysis Applications in Finance 305
18.1 Introduction and objectives 305
18.2 Solving tridiagonal systems 305
18.2.1 A tridiagonal solver in C++ 306
18.3 An introduction to interpolation 310
18.3.1 Polynomial interpolation 310
18.3.2 Rational function interpolation 311
18.3.3 Cubic spline interpolation 312
18.4 Summary and conclusions 313
19 Other Numerical Methods in Quantitative Finance 315
19.1 Introduction and objectives 315
19.2 The trinomial method for assets 315
19.3 Lattice data structures 318
19.4 Trinomial tree for the short rate 318
19.5 The multidimensional binomial method 321
19.6 Generic lattice structures 322
19.6.1 Candlestick charts 322
19.6.2 (Highly) generic lattice structures 324
19.7 Approximating exponential functions 326
19.8 Summary and conclusions 326
19.9 Exercises 326
20 The Monte Carlo Method Theory and C++ Frameworks 327
Dr. Joerg Kieritz and Daniel J. Duffy
20.1 Introduction and objectives 327
20.2 A short history of the Monte Carlo (MC) method 327
20.3 Examples of the application of the Monte Carlo method 327
20.3.1 Calculation of definite integrals 328
20.3.2 Device reliability 330
20.4 The Monte Carlo method in quantitative finance 333
20.4.1 An overview of stochastic differential equations (SDE) 333
20.4.2 Other background information 336
20.5 Software architecture for the Monte Carlo method 337
20.6 Examples and test cases 338
20.6.1 Plain options 338
20.6.2 Barrier options 338
20.6.3 Asian options 339
20.7 Summary and conclusions 340
20.8 Appendix: comparing Monte Carlo with other numerical methods 340
20.9 Exercises and projects 341

21 Skills Development: from White Belt to Black Belt 345
21.1 Introduction and objectives 345
21.2 Review of book 345
21.3 Part I: C++ essential skills 345
21.4 Part II: data structures, templates and patterns 346
21.5 Part III: applications in quantitative finance 347
21.6 Part IV: background information 347
21.7 Choosing a programming paradigm 348
21.7.1 Layer 1: foundation classes 348
21.7.2 Layer 2: mechanisms 348
21.7.3 Layer 3: building blocks 349
21.7.4 Layer 4: application level 349
21.8 Summary and conclusions 349
PART IV BACKGROUND INFORMATION 351
22 Basic C Survival Guide 353
22.1 Introduction and objectives 353
22.2 Basic data types 353
22.3 The C preprocessor 354
22.4 Pointers and references 355
22.5 Other useful bits and pieces 357
22.6 What to avoid in C 357
22.7 Test case: numerical integration in one dimension 358
22.8 Conclusions and summary 359
22.9 Exercises 359
23 Advanced C Syntax 363
23.1 Introduction and objectives 363
23.2 Fixed-size and dynamic arrays 364
23.3 Multi-dimensional arrays 364
23.4 Introduction to structures 365
23.5 Unions 366
23.6 Useful C libraries 366
23.7 Test case: linear regression 367
23.8 Conclusions and summary 370
23.9 Exercises 370
24 Datasim Visualisation Package in Excel: Drivers and Mechanisms 373
24.1 Introduction and objectives 373
24.2 Fundamental functionality in the package 373
24.3 Basic driver functionality 373
24.4 Excel mechanisms 376
24.5 Option values and sensitivities in excel 380
24.6 Finite difference method 384
24.7 Summary and conclusions 387
24.8 Exercises and projects 387

25 Motivating COM and Emulation in C++ 391
25.1 Introduction and objectives 391
25.2 A short history of COM 391
25.3 An introduction to multiple inheritance (MI) 391
25.4 Interfaces and multiple inheritance 396
25.5 Virtual function tables 399
25.6 Summary 399
26 COM Fundamentals 401
26.1 Introduction and objectives 401
26.2 Interfaces in COM 401
26.3 The IUnknown interface 401
26.4 Using IUnknown 402
26.4.1 Testing the interface 405
26.5 Defining new versions of components 406
26.6 Summary 406
References 407
Index 409