Modern Computational Finance AAD and Parallel Simulations

ANTOINE SAVINE is a mathematician and derivatives practitioner with leading investment banks. After globally running quantitative research in a major French bank for ten years, Antoine joined Jesper Andreasen to participate in the development of Danske Bank's award winning systems.Antoine also lectures in the University of Copenhagen's Masters of Science in Mathematics-Economics program, on topics including volatility modeling and numerical finance, for which this book is the curriculum. Antoine holds a Masters in Mathematics from the University of Paris-Jussieu and a PhD in Mathematics from the University of Copenhagen. He is best known for his work on volatility, multi-factor interest rate models, scripting, AAD and parallel Monte-Carlo. His computational finance books combine the unique insight of a leading practitioner with the rigor and pedagogy of an accomplished lecturer.

Modern Computational Finance xi

Preface by Leif Andersen xv

Acknowledgments xix

Introduction xxi

About the Companion C++ Code xxv

PART I Modern Parallel Programming 1

Introduction 3

CHAPTER 1 Effective C++ 17

CHAPTER 2 Modern C++ 25

2.1 Lambda expressions 25

2.2 Functional programming in C++ 28

2.3 Move semantics 34

2.4 Smart pointers 41

CHAPTER 3 Parallel C++ 47

3.1 Multi-threaded Hello World 49

3.2 Thread management 50

3.3 Data sharing 55

3.4 Thread local storage 56

3.5 False sharing 57

3.6 Race conditions and data races 62

3.7 Locks 64

3.8 Spinlocks 66

3.9 Deadlocks 67

3.10 RAII locks 68

3.11 Lock-free concurrent design 70

3.12 Introduction to concurrent data structures 72

3.13 Condition variables 74

3.14 Advanced synchronization 80

3.15 Lazy initialization 83

3.16 Atomic types 86

3.17 Task management 89

3.18 Thread pools 96

3.19 Using the thread pool 108

3.20 Debugging and optimizing parallel programs 113

PART II Parallel Simulation 123

Introduction 125

CHAPTER 4 Asset Pricing 127

4.1 Financial products 127

4.2 The Arbitrage Pricing Theory 140

4.3 Financial models 151

CHAPTER 5 Monte-Carlo 185

5.1 The Monte-Carlo algorithm 185

5.2 Simulation of dynamic models 192

5.3 Random numbers 200

5.4 Better random numbers 202

CHAPTER 6Serial Implementation 213

6.1 The template simulation algorithm 213

6.2 Random number generators 223

6.3 Concrete products 230

6.4 Concrete models 245

6.5 User interface 263

6.6 Results 268

CHAPTER 7 Parallel Implementation 271

7.1 Parallel code and skip ahead 271

7.2 Skip ahead with mrg32k3a 276

7.3 Skip ahead with Sobol 282

7.4 Results 283

PART III Constant Time Differentiation 285

Introduction 287

CHAPTER 8 Manual Adjoint Differentiation 295

8.1 Introduction to Adjoint Differentiation 295

8.2 Adjoint Differentiation by hand 308

8.3 Applications in machine learning and finance 315

CHAPTER 9 Algorithmic Adjoint Differentiation 321

9.1 Calculation graphs 322

9.2 Building and applying DAGs 328

9.3 Adjoint mathematics 340

9.4 Adjoint accumulation and DAG traversal 344

9.5 Working with tapes 349

CHAPTER 10 Effective AAD and Memory Management 357

10.1 The Node class 359

10.2 Memory management and the Tape class 362

10.3 The Number class 379

10.4 Basic instrumentation 398

CHAPTER 11 Discussion and Limitations 401

11.1 Inputs and outputs 401

11.2 Higher-order derivatives 402

11.3 Control flow 402

11.4 Memory 403

CHAPTER 12 Differentiation of the Simulation Library 407

12.1 Active code 407

12.2 Serial code 409

12.3 User interface 417

12.4 Serial results 424

12.5 Parallel code 426

12.6 Parallel results 433

CHAPTER 13 Check-Pointing and Calibration 439

13.1 Check-pointing 439

13.2 Explicit calibration 448

13.3 Implicit calibration 475

CHAPTER 14 Multiple Differentiation in Almost Constant Time 483

14.1 Multidimensional differentiation 483

14.2 Traditional Multidimensional AAD 484

14.3 Multidimensional adjoints 485

14.4 AAD library support 487

14.5 Instrumentation of simulation algorithms 494

14.6 Results 499

CHAPTER 15 Acceleration with Expression Templates 503

15.1 Expression nodes 504

15.2 Expression templates 507

15.3 Expression templated AAD code 524

Debugging AAD Instrumentation 541

Conclusion 547

References 549

Index 555

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