Modern Computational Finance

ANTOINE SAVINE is a mathematician and derivatives practitioner with 25 years of leadership experience with global investment banks. He wrote the book on automatic adjoint differentiation (AAD) and co-developed Differential Machine Learning. He was also influential in volatility modeling and many areas of numerical and computational finance. Antoine works with Superfly Analytics at Danske Bank, winner of the 2019 Excellence in Risk Management and Modelling RiskMinds award. He holds a PhD in Mathematical Finance from Copenhagen University, where he teaches quantitative and computational finance.Jesper Andreasen heads the Quantitative Research department at Saxo Bank. Over a 25 year long career he has held senior roles in quant departments of Bank of America, Nordea and General Re Financial Products, and he founded and headed the Superfly Analytics department at Danske Bank. Jesper co-received Risk magazine’s 2001 and 2012 Quant of the year awards and their In-House Risk System of the year award in 2015. He is an honorary professor of Mathematical Finance at Copenhagen University and completed his PhD in the same subject at Aarhus University in 1997.

“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

• My Life in Script by Jesper Andreasen xiPart I A Scripting Library in C++Introduction 3Chapter 1 Opening Remarks 7Introduction 71.1 Scripting is not only for exotics 121.2 Scripting is for cash-flows not payoffs 131.3 Simulation models 151.4 Pre-processing 171.5 Visitors 191.6 Modern implementation in C++ 211.7 Script templates 22Chapter 2 Expression Trees 252.1 In theory 252.2 In code 35Chapter 3 Visitors 413.1 The visitor pattern 413.2 The debugger visitor 473.3 The variable indexer 503.4 Pre-processors 543.5 Const visitors 553.6 The evaluator 573.7 Communicating with models 65Chapter 4 Putting Scripting Together with a Model 714.1 A simplistic Black-Scholes Monte-Carlo simulator 714.1.1 Random number generators 714.1.2 Simulation models 734.1.3 Simulation engines 764.2 Connecting the model to the scripting framework 76Chapter 5 Core Extensions and the “Pays” Keyword 815.1 In theory 815.2 In code 83Part II Basic ImprovementsIntroduction 93Chapter 6 Past Evaluator 95Chapter 7 Macros 97Chapter 8 Schedules of Cash-Flows 99Chapter 9 Support for Dates 105Chapter 10 Predefined Schedules and Functions 109Chapter 11 Support for Vectors 11311.1 Basic functionality 11311.2 Advanced functionality 11511.2.1 New node types 11611.2.2 Support in the parser 11611.2.3 Processing 11711.2.4 Evaluation 117Part III Advanced Improvements Introduction 121Chapter 12 Linear Products 12312.1 Interest rates and swaps 12312.2 Equities, foreign exchange, and commodities 12512.3 Linear model implementation 126Chapter 13 Fixed Income Instruments 12713.1 Delayed payments 12713.2 Discount factors 12813.3 The simulated data processor 12913.4 Indexing 12913.5 Upgrading “pays” to support delayed payments 13113.6 Annuities 13213.7 Forward discount factors 13213.8 Back to equities 13213.9 Libor and rate fixings 13313.10 Scripts for swaps and options 134Chapter 14 Multiple Underlying Assets 13714.1 Multiple assets 13714.2 Multiple currencies 139Chapter 15 American Monte-Carlo 14315.1 Least Squares Method 14315.2 One proxy 14715.3 Additional regression variables 14915.4 Feedback and exercise 14915.5 Multiple exercise and recursion 152Part IV Fuzzy Logic and Risk Sensitivities Introduction 157Chapter 16 Risk Sensitivities with Monte-Carlo 16116.1 Risk instabilities 16116.2 Two approaches toward a solution 16516.3 Smoothing for digitals and barriers 16616.4 Smoothing for scripted transactions 168Chapter 17 Support for Smoothing 169Chapter 18 An Automated Smoothing Algorithm 17518.1 Basic algorithm 17618.2 Nested and combined conditions 17918.3 Affected variables 17918.4 Further optimization 180Chapter 19 Fuzzy Logic 183Chapter 20 Condition Domains 18920.1 Fuzzy evaluation of discrete conditions 18920.1.1 Condition domains 18920.1.2 Constant conditions 19020.1.3 Boolean conditions 19120.1.4 Binary conditions 19320.1.5 Discrete conditions 19320.1.6 Putting it all together 19720.2 Identification of condition domains 19820.3 Constant expressions 201Chapter 21 Limitations 20321.1 Dead and alive 20321.2 Non-linear use of fuzzy variables 206Chapter 22 The Smoothing Factor 20922.1 Scripting support 20922.2 Automatic determination 211Part V Application to xVA Chapter 23 xVA 215Chapter 24 Branching 219Chapter 25 Closing Remarks 22325.1 Script examples 22325.2 Multi-threading and AAD 22825.3 Advanced LSM optimizations 229Appendix A Parsing 231A.1 Preparing for parsing 231A.2 Parsing statements 234A.3 Recursively parsing conditions 238A.4 Recursively parsing expressions 244A.5 Performance 252Bibliography 255Index 257