Implementing Models of Financial Derivatives: Object Oriented Applications with VBA

Implementing Models of Financial Derivatives: Object Oriented Applications with VBA......Page 5
Contents......Page 9
Preface......Page 17
PART I A PROCEDURAL MONTE CARLO METHOD IN VBA......Page 21
1.1 The Monte Carlo valuation method......Page 23
1.2 Issues with Monte Carlo......Page 28
1.3 Computational issues......Page 32
1.5 Exercises......Page 36
2.2 A high-level design......Page 39
2.3 Progressing towards the ideal......Page 41
2.5 Exercises......Page 42
3.1 Designing a Monte Carlo valuation application......Page 45
3.2 Deficiencies of the level 1 code......Page 55
3.4 Exercises......Page 56
4 Validation and Error Handling: Level 2......Page 59
4.1 Validation and error handling......Page 60
4.2 Encapsulating functionality......Page 65
4.3 The level 2 main ()......Page 68
4.4 Summary......Page 70
4.5 Exercises......Page 71
PART II OBJECTS AND POLYMORPHISM......Page 73
5.1 Objects in VBA......Page 75
5.2 An example: The StopWatch object......Page 83
5.3 Further helpful VBA features......Page 85
5.4 Objects in the Monte Carlo application......Page 87
5.6 Exercises......Page 98
6.1 Polymorphism......Page 101
6.2 Interfaces in VBA......Page 104
6.3 Implementing a polymorphic stopwatch......Page 106
6.4 Polymorphism and the Monte Carlo application......Page 108
6.5 Assessment of the polymorphic design......Page 120
6.7 Exercises......Page 122
7.1 The revised Monte Carlo application object......Page 127
7.2 The option object......Page 129
7.3 The evolver object......Page 133
7.5 Exercises......Page 136
8.1 Events......Page 139
8.2 The Level 5 Monte Carlo application......Page 142
8.3 The Factory object......Page 147
8.4 Output......Page 150
8.6 Exercises......Page 153
PART III USING FILES WITH VBA......Page 155
9.1 File handling in VBA......Page 157
9.2 The TextStream and FileSystemObject objects......Page 158
9.3 Intrinsic VB language functions......Page 163
9.4 Example: Reading and writing to sequential and random files......Page 165
9.6 Exercises......Page 171
10.1 Outline of the application......Page 173
10.2 Timings......Page 194
10.4 Exercises......Page 196
PART IV POLYMORPHIC FACTORIES IN VBA......Page 197
11.1 Using the VBE object library......Page 199
11.2 A simple factory illustration......Page 203
11.4 Exercises......Page 210
12.1 Conceptual features......Page 213
12.2 The polymorphic factory......Page 217
12.3 Using the Factory object......Page 226
12.4 Summary......Page 228
12.5 Exercises......Page 229
13.1 The structure of the application......Page 231
13.2 Meta-class objects......Page 232
13.3 The semi-polymorphic factory......Page 236
13.5 Exercises......Page 248
PART V PERFORMANCE ISSUES IN VBA......Page 251
14 Performance and Cost in VBA......Page 253
14.1 Arithmetic operations......Page 256
14.2 Procedure calls......Page 262
14.3 Data typing issues......Page 264
14.4 Summary......Page 267
14.5 Exercises......Page 268
15.1 Variations of the level 0 application......Page 269
15.2 Effect of level on times......Page 274
15.3 Summary......Page 278
15.4 Exercises......Page 279
16.1 Data structures in VBA......Page 281
16.2 Using VBA containers......Page 284
16.3 Numerical comparisons......Page 291
16.5 Exercises......Page 297
PART VI VARIANCE REDUCTION IN THE MONTE CARLO METHOD......Page 301
17.2 Antithetic variates......Page 303
17.3 Numerical assessment......Page 308
17.5 Exercises......Page 309
18.1 Stratified sampling......Page 311
18.3 Numerical assessment......Page 318
18.4 Summary......Page 324
18.5 Exercises......Page 325
19.1 Low-discrepancy sampling......Page 327
19.2 Implementing LD sampling......Page 330
19.3 Numerical assessment......Page 334
19.5 Exercises......Page 336
20.1 Control variates......Page 337
20.2 Examples of control variates......Page 339
20.3 Auxiliary model control variates......Page 345
20.5 Exercises......Page 351
21.1 A control variate application......Page 353
21.2 Numerical assessment......Page 358
21.4 Exercises......Page 364
22.1 Importance Sampling......Page 365
22.2 Valuing an OTM digital option......Page 366
22.3 Choices for the IS density......Page 368
22.4 Implementing importance sampling......Page 372
22.5 Numerical assessment......Page 382
22.7 Exercises......Page 388
23.1 Combining CV and IS......Page 391
23.2 Implementing variance reduction methods in combination......Page 392
23.3 Numerical assessment......Page 397
23.4 Summary......Page 404
23.5 Exercises......Page 406
PART VII THE MONTE CARLO METHOD: CONVERGENCE AND BIAS......Page 407
24.1 Reducing bias......Page 409
24.2 Bias reduction methods......Page 412
24.3 Bias and barrier options......Page 416
24.5 Exercises......Page 418
25.1 Discretization and convergence......Page 419
25.2 Ito–Taylor discretization schemes......Page 421
25.3 Schemes in 1-dimension......Page 426
25.4 Predictor–corrector simulation......Page 431
25.5 Numerical assessment for benchmark processes......Page 433
25.7 Exercises......Page 436
26.1 The CIR process......Page 437
26.2 Simulating discount factors......Page 444
26.4 Exercises......Page 449
27.1 Discretizing the Heston model......Page 451
27.2 Convergence in the Heston model......Page 455
27.3 Option valuation in the Heston model......Page 456
27.5 Exercises......Page 466
PART VIII VALUING AMERICAN OPTIONS BY SIMULATION......Page 467
28 Valuing American and Bermudan Options......Page 469
28.1 American options......Page 470
28.2 Monte Carlo and American options......Page 475
28.4 Exercises......Page 481
29.2 Choices for basis functions......Page 483
29.3 The early exercise boundary......Page 490
29.4 Effect on valuation......Page 493
29.5 Summary......Page 494
29.6 Exercises......Page 495
30.1 Implementation in VBA......Page 497
30.2 Valuing the American put?......Page 506
30.4 Exercises......Page 508
31.1 Control variates and the American put......Page 511
31.2 Control variates and the EEB......Page 518
31.3 A two-pass LSLS......Page 525
31.4 Summary......Page 529
31.5 Exercises......Page 531
Afterword......Page 533
APPENDICES......Page 535
A.1 Setting up Excel......Page 537
A.2 Compiler problems in VBA......Page 538
B.1 Geometrically averaged average rate options......Page 543
B.2 A quadratic payoff option......Page 546
B.3 A Bermudan option......Page 548
C.1 The utility procedures......Page 551
C.2 The complex number object......Page 560
C.3 Quadrature......Page 562
D Running DLLs from VBA......Page 565
E.1 Motivation for objects......Page 569
E.2 Properties of objects......Page 573
E.3 Implementing objects in VBA......Page 576
E.4 Patterns of object use......Page 579
E.5 Summary......Page 585
F.1 Lattice methods......Page 587
F.2 Implementing a level 0 lattice method......Page 590
F.3 Summary......Page 598
G.1 PDE methods for derivative valuation......Page 601
G.2 The Crank–Nicolson finite difference method......Page 602
G.3 Implementing Crank–Nicolson......Page 605
G.4 Assessment of the design......Page 611
G.5 Successive over-relaxation (SOR)......Page 615
G.6 Summary......Page 622
H.1 Root finding algorithms......Page 623
H.2 Minimization algorithms......Page 630
H.3 Summary......Page 632
VBA, Modelling, and Computing Glossary......Page 633
Abbreviations......Page 639
Coding, Notational, and Typographical Conventions......Page 641
Index to Code......Page 643
Index to Spreadsheets......Page 651
Index to Implementations......Page 653
Index to Library Functions......Page 657
Bibliography......Page 661
Index......Page 665