Financial Instrument Pricing Using C++

Financial Instrument Pricing Using C++......Page 4
Contents......Page 8
1.2 What’s special about this book?......Page 18
1.3 Who is this book for?......Page 19
1.4 Software requirements......Page 20
1.5 The structure of this book......Page 21
1.6 Pedagogical approach......Page 22
1.8 Source code on the CD......Page 23
PART I TEMPLATE PROGRAMMING IN C++......Page 24
2.1 Introduction and objectives......Page 26
2.2 Motivation and background......Page 27
2.3 Defining a template......Page 28
2.3.1 An example......Page 30
2.4 Template instantiation......Page 32
2.5 Function templates......Page 33
2.5.1 An example......Page 34
2.7 Guidelines when implementing templates......Page 35
2.8 Conclusions and summary......Page 36
3.2 A Bird’s-eye view of STL......Page 37
3.3 Sequence containers......Page 40
3.3.1 Programming lists......Page 41
3.3.2 Vectors and arrays in STL......Page 42
3.4.1 Sets in STL......Page 44
3.4.2 Maps in STL......Page 46
3.5.1 What kinds of iterators?......Page 47
3.6 Algorithms......Page 50
3.8 Conclusions and summary......Page 52
4.2 Clever data structures......Page 53
4.2.1 A simple output mechanism......Page 55
4.3 Set theory and STL......Page 57
4.4 Useful algorithms......Page 60
4.5 STL adaptor containers......Page 62
4.6 Conclusions and summary......Page 63
5.2 The Property pattern......Page 64
5.2.1 Requirements for a Property pattern......Page 65
5.3 An example......Page 68
5.4 Extending the Property pattern: property sets and property lists......Page 69
5.4.1 An example......Page 72
5.5.1 Example: Executive options......Page 74
5.6 Conclusions and summary......Page 76
PART II BUILDING BLOCK CLASSES......Page 78
6.1 Introduction and objectives......Page 80
6.2 Motivation and background......Page 81
6.4 The Array and Matrix classes in detail......Page 83
6.4.1 Simple print functions......Page 86
6.4.2 Array example......Page 87
6.4.3 Matrix example......Page 88
6.5 The Vector and NumericMatrix classes in detail......Page 89
6.6 Associative arrays and matrices......Page 91
6.7 Conclusions and summary......Page 94
7.2 An overview of the functionality......Page 95
7.3.3 Reliability......Page 96
7.4 The core processes......Page 97
7.4.1 Interactions between matrices and vectors......Page 100
7.4.2 Some examples......Page 101
7.5.1 Measures of central tendency......Page 102
7.5.3 Moments, skewness, kurtosis......Page 103
7.6 Using the functions......Page 104
7.7 An introduction to exception handling......Page 105
7.7.1 Try, throw and catch: A bit like tennis......Page 106
7.8 Conclusions and summary......Page 107
8.2 An introduction to numerical linear algebra......Page 108
8.2.2 Iterative methods......Page 110
8.3.1 LU decomposition......Page 111
8.3.2 Godunov’s Double Sweep method......Page 114
8.4 Block tridiagonal systems......Page 116
8.5.1 Positive-definite matrices and diagonal dominance......Page 118
8.6 Conclusions and summary......Page 119
9.2 Function pointers in C++......Page 120
9.3 Function objects in STL......Page 123
9.3.2 STL and financial engineering......Page 125
9.4 Some function types......Page 126
9.5 Creating your own function classes......Page 128
9.6 Arrays of functions......Page 131
9.8 Real-valued functions......Page 132
9.10 Conclusions and summary......Page 133
10.2 Discrete and continuous probability distribution functions......Page 134
10.3.1 Uniform (rectangular) distribution......Page 136
10.3.2 Normal distribution......Page 138
10.3.4 Gamma distribution and its specialisations......Page 139
10.4.1 Poisson distribution......Page 141
10.4.2 Binomial and Bernoulli distributions......Page 142
10.4.3 Pascal and geometric distributions......Page 143
10.5.2 Discrete distributions......Page 144
10.6 Conclusions and summary......Page 145
PART III ORDINARY AND STOCHASTIC DIFFERENTIAL EQUATIONS......Page 146
11.1 Introduction and objectives......Page 148
11.2.1 Qualitative properties of the solution......Page 149
11.3 Discretisation......Page 150
11.4 Common schemes......Page 151
11.5 Some theoretical issues......Page 153
11.6 Fitting: Special schemes for difficult problems......Page 154
11.7 Non-linear scalar problems and predictor–corrector methods......Page 155
11.8 Extrapolation techniques......Page 156
11.9 C++ design and implementation......Page 157
11.10 Generalisations......Page 160
11.11 Conclusions and summary......Page 161
12.2.1 Random variables......Page 162
12.2.2 Generating random variables......Page 164
12.2.3 Random (stochastic) processes......Page 167
12.3 An introduction to stochastic differential equations......Page 168
12.4 Some finite difference schemes......Page 169
12.5 Which scheme to use?......Page 170
12.7 Conclusions and summary......Page 171
13.2 Description of problem......Page 172
13.3 (Traditional) centred-difference schemes......Page 174
13.4 Approximation of the boundary conditions......Page 175
13.4.1 Linearity boundary condition......Page 176
13.6 Approximating the derivatives......Page 177
13.7 Design issues......Page 178
13.8 Conclusions and summary......Page 180
14.1 Introduction and objectives......Page 181
14.3 The Jacobi method......Page 182
14.6 Other methods......Page 183
14.6.3 Solving sparse systems of equations......Page 184
14.7 The linear complementarity problem......Page 185
14.8 Implementation......Page 186
14.9 Conclusions and summary......Page 188
PART IV PROGRAMMING THE BLACK–SCHOLES ENVIRONMENT......Page 190
15.2 The development life cycle......Page 192
15.3 Partial differential equations......Page 193
15.4 Numerical approximation of PDEs......Page 194
15.6 Special schemes for special problems......Page 196
15.8 Origins and application areas......Page 197
15.9 Conclusions and summary......Page 198
16.2 Model problem: The one-dimensional heat equation......Page 199
16.3 The Black–Scholes equation......Page 203
16.4 Initial conditions and exotic options payoffs......Page 204
16.4.1 Payoff functions in options modelling......Page 205
16.6 Method of lines: A whirlwind introduction......Page 207
16.7 Conclusions and summary......Page 208
17.1 Introduction and objectives......Page 209
17.2 Fully implicit method......Page 210
17.3 An introduction to the Crank–Nicolson method......Page 211
17.4.1 How are derivatives approximated?......Page 212
17.4.2 Boundary conditions......Page 214
17.4.4 Proving stability......Page 215
17.5 Is there hope? the Keller scheme......Page 216
17.5.1 The advantages of the Box scheme......Page 218
17.6 Conclusions and summary......Page 219
18.2.1 A new class of robust difference schemes......Page 220
18.3.1 The fitted scheme in more detail: Main results......Page 222
18.4.1 Graceful degradation......Page 225
18.5.1 An explicit time-marching scheme......Page 226
18.6 Exponential fitting and exotic options......Page 227
18.7 Some final remarks......Page 228
19.1 Introduction and objectives......Page 229
19.2 Modelling partial differential equations in C++......Page 231
19.2.1 Function classes in C++......Page 232
19.2.2 Function classes for partial differential equations......Page 234
19.3 Finite difference schemes as C++ classes, Part I......Page 235
19.4 Finite difference schemes as C++ classes, Part II......Page 236
19.5.1 Functions and parameters......Page 237
19.5.2 The main program......Page 238
19.7 Conclusions and summary......Page 241
20.1 Introduction and objectives......Page 242
20.2 A model problem......Page 243
20.3 Motivation and history......Page 244
20.4 Basic ADI scheme for the heat equation......Page 245
20.4.1 Three-dimensional heat equation......Page 246
20.5 Basic splitting scheme for the heat equation......Page 247
20.6 Approximating cross-derivatives......Page 248
20.7 Handling boundary conditions......Page 249
20.8 Algorithms and design issues......Page 251
20.9 Conclusions and summary......Page 253
21.2.1 Asian options......Page 254
21.2.3 Options with two underlying assets......Page 256
21.2.4 Basket options......Page 257
21.3 Finite difference approximations......Page 258
21.4.1 Upwinding......Page 259
21.6 Conclusions and summary......Page 260
PART V DESIGN PATTERNS......Page 262
22.1 Introduction and objectives......Page 264
22.2 Input mechanisms......Page 265
22.3 Conversion and processing mechanisms......Page 266
22.4 Output and display mechanisms......Page 267
22.4.1 Ensuring that Excel is started only once......Page 268
22.7 Other functionality......Page 269
22.7.1 Accessing cell data......Page 271
22.7.3 Using Excel with finite difference schemes......Page 272
22.8 Using Excel and property sets......Page 275
22.9 Extensions and the road to design patterns......Page 276
22.10 Conclusions and summary......Page 277
23.1 Introduction and objectives......Page 278
23.2.1 The templated Singleton solution......Page 280
23.2.2 An extended example......Page 283
23.2.3 Applications to financial engineering......Page 286
23.3 The Prototype pattern......Page 287
23.3.2 Applications to financial engineering......Page 288
23.4 Factory Method pattern (virtual constructor)......Page 289
23.4.1 An extended example......Page 291
23.5 Abstract Factory pattern......Page 292
23.5.2 An extended example......Page 294
23.7 Conclusions and summary......Page 296
24.2 Kinds of structural relationships between classes......Page 298
24.2.1 Aggregation......Page 299
24.2.2 Association......Page 300
24.3 Whole–Part pattern......Page 303
24.4 The Composite pattern......Page 305
24.5 The Façade pattern......Page 306
24.6.1 An example of the Bridge pattern......Page 307
24.7 Conclusions and summary......Page 312
25.1 Introduction and objectives......Page 313
25.2 Kinds of behavioural patterns......Page 314
25.3 Iterator pattern......Page 315
25.3.1 Iterating in composites......Page 316
25.3.2 Iterating in property sets......Page 317
25.4 The Visitor pattern......Page 318
25.4.1 Visitors and the Extensible Markup Language (XML)......Page 319
25.5 Notification patterns......Page 322
25.6 Conclusions and summary......Page 324
PART VI DESIGN AND DEPLOYMENT ISSUES......Page 326
26.1.1 What’s the big deal with XML?......Page 328
26.3.1 XML files......Page 329
26.3.2 XML syntax......Page 330
26.3.3 Attributes in XML......Page 331
26.4.1 DTD syntax......Page 332
26.4.2 Validation issues......Page 336
26.5 Extensible Stylesheet Language Transformation (XSLT)......Page 337
26.5.1 Namespaces in XML......Page 338
26.5.2 Main concepts in XSL......Page 339
26.6.1 Product architecture overview......Page 341
26.6.2 Example: Equity derivative options product architecture......Page 343
26.7 Conclusions and summary......Page 344
27.2 XML Schema......Page 345
27.2.1 Element declaration......Page 346
27.2.2 User-defined simple and complex types......Page 347
27.2.3 Multiplicity issues......Page 348
27.2.4 An example......Page 349
27.3 Accessing XML data: The Document Object Model......Page 351
27.4 DOM and C++: The essentials......Page 352
27.5 DOM, entities and property sets......Page 355
27.5.1 XML readers and writers......Page 357
27.6 XML structures for plain and barrier options......Page 359
27.7 Conclusions and summary......Page 362
28.2 Object model in Excel: An overview......Page 363
28.3.1 Startup......Page 365
28.3.2 Creating charts and cell values......Page 366
28.3.3 Interoperability with the SimplePropertySet......Page 367
28.4 Implementing the core process......Page 368
28.4.2 Calculations......Page 369
28.4.3 Displaying the results of the calculations......Page 370
28.5 Extensions......Page 371
28.7 Conclusions and summary......Page 372
29.2 Status report and new requirements......Page 373
29.3.1 What kinds of add-ins are there?......Page 374
29.4 Automation add-in in detail......Page 376
29.4.1 Functions with two parameters......Page 379
29.4.2 Functions that accept a range......Page 381
29.4.3 Using the Vector template class......Page 383
29.5 Creating a COM add-in......Page 384
29.7 Conclusions and summary......Page 390
30.2 Spreads......Page 391
30.3 Combinations: Straddles and strangles......Page 392
30.4 Designing and implementing spreads......Page 393
30.5 Delta hedging......Page 395
30.6 An example......Page 396
30.7 Tips and guidelines......Page 398
A1 My C++ refresher......Page 400
A2 Dates and other temporal types......Page 411
References......Page 414
Index......Page 418