My Life in Script by Jesper Andreasen xi Part I A Scripting Library in C++ Introduction 3 Chapter 1 Opening Remarks 7 Introduction 7 1.1 Scripting is not only for exotics 12 1.2 Scripting is for cash-flows not payoffs 13 1.3 Simulation models 15 1.4 Pre-processing 17 1.5 Visitors 19 1.6 Modern implementation in C++ 21 1.7 Script templates 22 Chapter 2 Expression Trees 25 2.1 In theory 25 2.2 In code 35 Chapter 3 Visitors 41 3.1 The visitor pattern 41 3.2 The debugger visitor 47 3.3 The variable indexer 50 3.4 Pre-processors 54 3.5 Const visitors 55 3.6 The evaluator 57 3.7 Communicating with models 65 Chapter 4 Putting Scripting Together with a Model 71 4.1 A simplistic Black-Scholes Monte-Carlo simulator 71 4.1.1 Random number generators 71 4.1.2 Simulation models 73 4.1.3 Simulation engines 76 4.2 Connecting the model to the scripting framework 76 Chapter 5 Core Extensions and the “Pays” Keyword 81 5.1 In theory 81 5.2 In code 83 Part II Basic Improvements Introduction 93 Chapter 6 Past Evaluator 95 Chapter 7 Macros 97 Chapter 8 Schedules of Cash-Flows 99 Chapter 9 Support for Dates 105 Chapter 10 Predefined Schedules and Functions 109 Chapter 11 Support for Vectors 113 11.1 Basic functionality 113 11.2 Advanced functionality 115 11.2.1 New node types 116 11.2.2 Support in the parser 116 11.2.3 Processing 117 11.2.4 Evaluation 117 Part III Advanced Improvements Introduction 121 Chapter 12 Linear Products 123 12.1 Interest rates and swaps 123 12.2 Equities, foreign exchange, and commodities 125 12.3 Linear model implementation 126 Chapter 13 Fixed Income Instruments 127 13.1 Delayed payments 127 13.2 Discount factors 128 13.3 The simulated data processor 129 13.4 Indexing 129 13.5 Upgrading “pays” to support delayed payments 131 13.6 Annuities 132 13.7 Forward discount factors 132 13.8 Back to equities 132 13.9 Libor and rate fixings 133 13.10 Scripts for swaps and options 134 Chapter 14 Multiple Underlying Assets 137 14.1 Multiple assets 137 14.2 Multiple currencies 139 Chapter 15 American Monte-Carlo 143 15.1 Least Squares Method 143 15.2 One proxy 147 15.3 Additional regression variables 149 15.4 Feedback and exercise 149 15.5 Multiple exercise and recursion 152 Part IV Fuzzy Logic and Risk Sensitivities Introduction 157 Chapter 16 Risk Sensitivities with Monte-Carlo 161 16.1 Risk instabilities 161 16.2 Two approaches toward a solution 165 16.3 Smoothing for digitals and barriers 166 16.4 Smoothing for scripted transactions 168 Chapter 17 Support for Smoothing 169 Chapter 18 An Automated Smoothing Algorithm 175 18.1 Basic algorithm 176 18.2 Nested and combined conditions 179 18.3 Affected variables 179 18.4 Further optimization 180 Chapter 19 Fuzzy Logic 183 Chapter 20 Condition Domains 189 20.1 Fuzzy evaluation of discrete conditions 189 20.1.1 Condition domains 189 20.1.2 Constant conditions 190 20.1.3 Boolean conditions 191 20.1.4 Binary conditions 193 20.1.5 Discrete conditions 193 20.1.6 Putting it all together 197 20.2 Identification of condition domains 198 20.3 Constant expressions 201 Chapter 21 Limitations 203 21.1 Dead and alive 203 21.2 Non-linear use of fuzzy variables 206 Chapter 22 The Smoothing Factor 209 22.1 Scripting support 209 22.2 Automatic determination 211 Part V Application to xVA Chapter 23 xVA 215 Chapter 24 Branching 219 Chapter 25 Closing Remarks 223 25.1 Script examples 223 25.2 Multi-threading and AAD 228 25.3 Advanced LSM optimizations 229 Appendix A Parsing 231 A.1 Preparing for parsing 231 A.2 Parsing statements 234 A.3 Recursively parsing conditions 238 A.4 Recursively parsing expressions 244 A.5 Performance 252 Bibliography 255 Index 257

PRAISE FOR MODERN COMPUTATIONAL FINANCE “This book is an indispensable resource for any quant. ­Written by experts in the field and filled with practical examples and industry insights that are hard to find elsewhere, the book sets a new standard for computational finance.” —Paul Glasserman, Jack R. Anderson Professor of Business, Columbia University “The global financial crisis resulted in profound changes to quants’ Modus Operandi. Modern Computational Finance describes some of the tools necessary to deal with these changes. This book covers in detail several important topics of interest to anyone who wants to stay au ­courant with modern developments in financial engineering. While the book is ­predominantly practically oriented, it strikes a fine balance between theoretical and applied considerations. The authors are prominent practitioners and undisputed thought-leaders in the field. I recommend this book enthusiastically to anyone who wishes to understand the current and emerging trends in financial engineering.” —Professor Alexander Lipton, Fellow, Connection Science and Engineering, Massachusetts Institute of Technology; Founder and CIO, Sila “This is a new era that expects a new, expanded skill set from a new ­generation of quants. This is a new type of publication that combines words, mathematics, and code to offer a full picture for the generic, effective, practical development of modern financial libraries. The authors ­provide the unique perspective of long-time leading derivatives practitioners. Brilliant.” —Rolf Poulsen, Professor of Mathematical Finance, University of ­Copenhagen

“The Global Financial Crisis resulted in profound changes in quants’ Modus Operandi. This timely three-volume set describes some of the tools necessary to deal with these changes. Individual volumes cover in detail several important topics of interest to anyone who wants to stay au courant with modern developments in financial engineering. While the books are predominantly practically oriented, they strike a fine balance between theoretical and applied considerations. The authors are prominent practitioners and indisputable thought-leaders in the field. I recommend this set enthusiastically to anyone who wishes to understand the current and emerging trends in financial engineering.” - Prof. Alexander Lipton, Founder and CEO, Stronghold Labs; Fellow, Connection Science and Engineering, Massachusetts Institute of Technology