Scripting of derivatives transactions has been a central piece of financial software since the 1990s. Most derivatives valuation and risk systems, either in-house or from external vendors, feature scripting technology. Yet, the expertise in this field remains unwritten to date, without any dedicated article or publication.

This volume fills the gap. It is written by Jesper Andreasen and Antoine Savine, who have developed scripting systems for leading investment banks since the 1990s, actively contributed to the development of the scripting technology, and co-developed Danske Bank’s award-winning derivatives system.The publication comes with a complete, professional scripting library written in modern C++, and the chapters gradually and pedagogically guide readers towards its construction.

Scripting technology is widely considered as a convenience for the structuring and risk management of exotic derivatives, only. This publication shows that the scripting technology has much wider applications. Specifically, it demonstrates how scripting provides a unique representation of financial transactions that enables the user to interrogate, aggregate and manipulate cash-flows in multiple ways, facilitating portfolio-wide risk assessment and regulatory calculations like XVA. This is essential reading for developers and analysts, all professionals involved with financial derivatives, as well as students and teachers in Masters and PhD programs in finance.

ANTOINE SAVINE is a mathematician and derivatives practitioner with leading investment banks since 1995. Antoine was the Global Head of Fixed Income Derivatives Research for BNP-Paribas for 10 years, and presently works with Danske Bank, whose xVA system won the In-House System of the Year 2015 Risk Award. Antoine’s Computational Finance books provide a unique practitioner insight into the implementation of derivatives models.

Antoine lectures in the University of Copenhagen’s Masters of Science in Mathematics-Economics, including Volatility Modeling and Numerical Finance, for which his book AAD and Parallel Simulations is the curriculum.

Antoine holds a Masters from the University of Paris (Jussieu) and a PhD from the University of Copenhagen, both in Mathematics. He is best known for his work on volatility, multi-factor interest rate models, scripting, AAD and parallel Monte-Carlo.

JESPER ANDREASEN heads the Quantitative Research Department at Saxo Bank in Copenhagen. Prior to this, Jesper has held senior positions at the quantitative research departments of Danske Bank, Bank of America, Nordea and General Re Financial Products. Jesper's current research interests include real-time risk and capital calculations, IT implementation, statistics, and trading strategies. Jesper earned a PhD in mathematical finance from Aarhus University, Denmark, in 1997. He received Risk Magazine’s Quant of the Year awards in 2001 and 2012, joint with Leif Andersen and Brian Huge respectively, and is an honorary professor of mathematical finance at Copenhagen University.

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