C++ for Financial Mathematics

Cover....1

Half Title....2

Title Page....6

Copyright Page....7

Contents....8

Introduction....18

1 Getting Started....24

1.1 Installing your development environment....24

1.1.1 For Windows....24

1.1.2 For Unix....24

1.1.3 For MacOS X....24

1.2 Running an example program....25

1.3 Compiling and running the code....26

1.3.1 Compiling on Windows....27

1.3.2 Compiling on Unix....29

1.4 Understanding the example code....31

1.5 Configuring the compiler....35

1.6 Making decisions....36

1.7 Exercises....37

1.8 Summary....38

2 Basic Data Types and Operators....40

2.1 Memory terminology....40

2.2 Basic data types....41

2.2.1 Integers....41

2.2.2 Floating point numbers....43

2.2.3 Booleans....43

2.2.4 Characters....43

2.3 Casting....45

2.4 Memory addresses....49

2.5 Operators....51

2.5.1 The sizeof operator....51

2.5.2 Mathematical operations....51

2.5.3 Comparison operators....52

2.5.4 Logical operators....52

2.5.5 Bitwise operators....52

2.5.6 Combining operators....53

2.5.7 Assignment operators....53

2.5.8 If statements revisited....55

2.6 Summary....58

3 Functions....60

3.1 The C++ function syntax....60

3.2 Recursion....64

3.3 Libraries....65

3.4 Declaring and defining functions....65

3.5 Functions that don’t return a value....67

3.6 Specifying default values....68

3.7 Overloading functions....69

3.8 Global and local variables....70

3.9 Namespaces....71

3.10 Summary....75

4 Flow of Control....78

4.1 while loops....78

4.2 do-while loops....80

4.3 for loops....81

4.4 break, continue, return....83

4.5 throw statements....84

4.6 switch statements....86

4.7 Scope....88

4.8 Flow of control in operators....88

4.8.1 Short circuit evaluation....89

4.8.2 The ternary operator....89

4.8.3 The comma operator....90

4.9 Summary....92

5 Working with Multiple Files....94

5.1 The project FMLib....94

5.2 Header files....95

5.3 Creating our project....96

5.3.1 Creating the first header file....96

5.3.2 Some code that uses the functions....98

5.3.3 Write the definitions....99

5.4 How header files work....100

5.4.1 The meaning of include....100

5.4.2 Pragma once....100

5.4.3 Information hiding....101

5.4.4 Inline....103

5.5 A complete example....104

5.6 Summary....105

6 Unit Testing....108

6.1 A testing framework for C++....109

6.2 Macros....109

6.3 The macros in testing.h....110

6.3.1 The ASSERT macro....110

6.3.2 The ASSERT_APPROX_EQUAL macro....110

6.3.3 The INFO macro....111

6.3.4 The DEBUG_PRINT macro....111

6.3.5 The TEST macro....112

6.4 Using testing.h....112

6.5 What have we gained?....114

6.6 Testing normcdf....115

6.7 Summary....117

7 Using C++ Classes....120

7.1 Vectors....120

7.2 Pass by reference and const....123

7.2.1 Pass by reference....124

7.2.2 The const keyword....125

7.2.3 Pass by reference without const....127

7.3 Using ofstream....127

7.4 Working with string....129

7.5 Building strings efficiently....130

7.6 Writing a pie chart....131

7.6.1 A web-based chart....132

7.6.2 Create a header file....134

7.6.3 Write a source file....135

7.6.4 Enable testing in your files....135

7.6.5 Write functions to generate the boiler plate....135

7.6.6 Write a simple version of the chart data....136

7.6.7 Write a test of what we’ve done so far....137

7.6.8 Write the interesting code....137

7.6.9 Testing the interesting code....138

7.6.10 Wrap it all up into a single function....139

7.7 The architecture of the World Wide Web....140

7.8 Summary....144

8 User-Defined Types....146

8.1 Terminology....146

8.2 Writing your own class....147

8.2.1 Writing the declaration....147

8.2.2 Using a class....149

8.2.3 Passing objects between functions....150

8.2.4 How have classes helped?....150

8.3 Adding functions to classes....151

8.3.1 Using const on member functions....153

8.4 A financial example....154

8.4.1 What have we gained?....156

8.5 Recommendations on writing classes....157

8.6 Encapsulation....158

8.6.1 Implementing PieChart....160

8.6.2 Using PieChart....160

8.7 Constructors....161

8.7.1 Writing a default constructor....162

8.7.2 An alternative, and superior syntax....163

8.8 Constructors with parameters....164

8.9 Summary....167

9 Monte Carlo Pricing in C++....168

9.1 A function to simulate stock prices....169

9.2 Writing a Monte Carlo pricer....174

9.3 Generating random numbers for Monte Carlo....177

9.4 Summary....181

10 Interfaces....182

10.1 An interface for pricing options....182

10.2 Describing an interface in C++....184

10.3 Examples of interfaces....187

10.4 Interfaces in object-oriented programming....189

10.5 What’s wrong with if statements?....191

10.6 An interface for integration....192

10.7 Summary....196

11 Arrays, Strings, and Pointers....198

11.1 Arrays, the C alternative to vector....199

11.2 Pointers....202

11.2.1 new and delete....202

11.2.2 Pointer operators....203

11.2.3 Looping with pointers....205

11.2.4 Using pointers in practice....208

11.3 Pointers to text....208

11.4 Pass by pointer....210

11.5 Don’t return pointers to local variables....212

11.6 Using pointers to share data....214

11.6.1 Sharing with shared_ptr....217

11.7 Sharing data with references....220

11.8 The C++ memory model....222

11.8.1 The stack....223

11.8.2 The heap....225

11.9 Summary....227

12 More Sophisticated Classes....228

12.1 Inlining member functions....228

12.2 The this keyword....229

12.3 Inheritance....230

12.3.1 What have we gained?....232

12.3.2 Terminology....232

12.4 Overriding methods — the virtual keyword....233

12.4.1 A note on the keyword virtual....234

12.5 Abstract functions =0....235

12.6 Multiple layers....235

12.6.1 UML....236

12.6.2 Another object hierarchy....238

12.6.3 Multiple inheritance....238

12.6.4 Calling superclass methods....239

12.7 Forward declarations and the structure of cpp files....240

12.8 The static keyword....241

12.9 The protected keyword....243

12.10 Summary....245

13 The Portfolio Class....246

13.1 The Priceable interface....246

13.2 The Portfolio interface and implementation....247

13.2.1 Implementation of PortfolioImpl....250

13.3 Testing....251

13.4 UML....253

13.5 Limitations....254

13.6 Summary....255

14 Delta Hedging....256

14.1 Discrete-time delta hedging....256

14.2 Implementing the delta hedging strategy in C++....258

14.2.1 Class declaration....258

14.2.2 Implementation of runSimulation....260

14.2.3 Implementing the other methods of HedgingSimulator....261

14.2.4 Changes to CallOption....263

14.3 Testing the simulation....264

14.4 Interpreting and extending our simulation....264

14.5 Summary....267

15 Debugging and Development Tools....268

15.1 Debugging strategies....268

15.1.1 Unit tests....268

15.1.2 Reading your code....269

15.1.3 Logging statements....269

15.1.4 Using a debugger....270

15.1.5 Divide and conquer....270

15.2 Debugging with Visual Studio....271

15.2.1 Obtaining a stack trace in Visual Studio....271

15.2.2 Breakpoints and single stepping in Visual Studio....273

15.3 Debugging with GDB....275

15.3.1 Using GDB to obtain a stack trace....276

15.3.2 Breakpoints and single stepping with GDB....279

15.3.3 Other commands and features....280

15.4 Other development tools and practices....281

15.4.1 Version control....281

15.4.2 Bug tracking....282

15.4.3 Testing framework....282

15.4.4 Automated build....283

15.4.5 Continuous integration....284

15.4.6 Logging....284

15.4.7 Static analysis....284

15.4.8 Memory-leak detection....285

15.4.9 Profiling tools....285

15.4.10 Example....286

15.5 Summary....287

16 A Matrix Class....290

16.1 Basic functionality of Matrix....290

16.2 The constructor and destructor of Matrix....292

16.2.1 Virtual destructors....294

16.2.2 When is a destructor needed?....295

16.2.3 Additional constructors....296

16.3 Const pointers....297

16.4 Operator overloading....298

16.4.1 Overloading +....298

16.4.2 Overloading other arithmetic operators....300

16.4.3 Overloading comparison operators....301

16.4.4 Overloading the << operator....302

16.4.4.1 Remarks on return by reference....303

16.4.5 Overloading the () operator....303

16.4.6 Overloading +=....304

16.5 The rule of three....305

16.5.1 Overriding the assignment operator....305

16.5.2 Writing a copy constructor....306

16.5.3 The easy way to abide by the rule of three....307

16.5.4 Move operators....308

16.6 Completing the Matrix class....308

16.7 Array Programming....309

16.7.1 Implementing an efficient matrix class....309

16.7.2 Array programming....310

16.7.3 Array programming in the option classes....311

16.7.4 Array programming for the BlackScholesModel....312

16.7.5 Array programming the Monte Carlo pricer....313

16.7.6 Performance....313

16.8 Summary....315

17 An Overview of Templates....318

17.1 Template functions....318

17.2 Template classes....320

17.3 Templates as an alternative to interfaces....322

17.4 Summary....325

18 The Standard Template Library....326

18.1 typedef....327

18.2 auto....329

18.3 Using iterators with vectors....330

18.4 for loops and containers....332

18.5 The container set....333

18.6 The container vector....334

18.7 The container list....335

18.8 The container initializer_list....338

18.9 The containers map and unordered_map....338

18.9.1 How a map works....340

18.9.2 How an unordered_map works....341

18.10 Storing complex types in containers....343

18.11 A mathematical model for multiple stocks....343

18.12 Using the Standard Template Library in FMLib....345

18.13 Summary....350

19 Function Objects and Lambda Functions....352

19.1 Function objects....352

19.2 Lambda functions....353

19.3 Function pointers....356

19.4 Sorting with lambda functions....357

19.5 Summary....359

20 Threads....360

20.1 Concurrent programming in C++....361

20.1.1 Creating threads....361

20.1.2 Mutual exclusion....362

20.1.3 Global variables and race conditions....365

20.1.4 Problems with locking....366

20.2 The command design pattern....369

20.3 Monte Carlo pricing....370

20.3.1 Random number generation with multiple threads....371

20.3.2 A multi-threaded pricer....372

20.3.3 Implementing Task....373

20.3.4 Using the Executor....374

20.3.5 Remarks upon the design....374

20.4 Coordinating threads....375

20.4.1 The Pipeline pattern....375

20.4.2 How Pipeline is implemented....378

20.5 Summary....381

21 Next Steps....382

21.1 Programming....382

21.1.1 Libraries....382

21.1.2 Software development....382

21.1.3 C++ language features....383

21.1.4 Other languages....383

21.2 Financial mathematics....384

A Risk-Neutral Pricing....386

A.1 The players in financial markets....386

A.2 Derivatives contracts....389

A.3 Risk-neutral pricing....393

A.4 Modelling stock prices....395

A.5 Monte Carlo pricing....400

A.6 Hedging....402

A.7 Summary....405

Bibliography....406

Index....408

If you know a little bit about financial mathematics but don’t yet know a lot about programming, then C++ for Financial Mathematics is for you.

C++ is an essential skill for many jobs in quantitative finance, but learning it can be a daunting prospect. This book gathers together everything you need to know to price derivatives in C++ without unnecessary complexities or technicalities. It leads the reader step-by-step from programming novice to writing a sophisticated and flexible financial mathematics library. At every step, each new idea is motivated and illustrated with concrete financial examples.

As employers understand, there is more to programming than knowing a computer language. As well as covering the core language features of C++, this book teaches the skills needed to write truly high quality software. These include topics such as unit tests, debugging, design patterns and data structures.

The book teaches everything you need to know to solve realistic financial problems in C++. It can be used for self-study or as a textbook for an advanced undergraduate or master’s level course.