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Modern Computational Finance: AAD and Parallel Simulations

Modern Computational Finance: AAD and Parallel Simulations

  • Author:
  • Publisher: John Wiley & Sons
  • ISBN: 9781119539452
  • Published In: November 2018
  • Format: Hardback , 592 pages
  • Jurisdiction: International ? Disclaimer:
    Countri(es) stated herein are used as reference only

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    Arguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware.

    AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance.

    Danske Bank's wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank's systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives software.

    This volume is a complete, self-contained learning reference for AAD, and its application in finance. AAD is explained in deep detail throughout chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation and acceleration with expression templates.

    The book comes with professional source code in C++, including an efficient, up to date implementation of AAD and a generic parallel simulation library. Modern C++, high performance parallel programming and interfacing C++ with Excel are also covered. The book builds the code step-by-step, while the code illustrates the concepts and notions developed in the book.

  • 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

  • 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.

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