CHAPTER 1
A Tour of C++ and Environs

riverrun, past Eve and Adam's, from swerve of shore to bend of bay, brings us by a commodius vicus of recirculation back to Howth Castle and Environs

—Joyce (1939)

1.1 Introduction and Objectives

This book is the second edition of Financial Instrument Pricing Using C++, also written by the author (Duffy, 2004B). The most important reason for writing this hands-on book is to reflect the many changes and improvements to the C++ language, in particular due to the announcement of the new standard C++11 (and to a lesser extent C++14 and C++17). It feels like a new language compared to C++03 and in a sense it is. First, C++11 improves and extends the syntax of C++03. Second, it has become a programming language that supports the functional programming model in addition to the object-oriented and generic programming models.

We apply modern C++ to design and implement applications in computational finance, in particular option pricing problems using partial differential equation (PDE)/finite difference method (FDM), Monte Carlo and lattice models. We show the benefits of using C++11 compared to similar solutions in C++03. The resulting code tends to be more maintainable and extendible, especially if the software system has been properly designed. We recommend spending some time on designing the software system before jumping into code and to this end we include a defined process to take a problem description, design the problem and then implement it in such a way that it results in a product that satisfies the requirements and that is delivered on time and within budget.

This book is a detailed exposition of the language features in C++, how to use these features and how to design applications in computational finance. We discuss modern numerical methods to price plain and American options and the book is written in a hands-on, step-by-step fashion.

1.2 What is C++?

C++ is a general-purpose systems programming language that was originally designed as an extension to the C programming language. Its original name was ‘C with classes' and its object-oriented roots can be traced to the programming language Simula which was one of the first object-oriented languages. C++ was standardised by the International Organization for Standardization (ISO) in 1998 (called the C++03 standard) and C++14 is the standard at the moment of writing. It can be seen as a minor extension to C++11 which is a major update to the language.

C++ was designed primarily for applications in which performance, efficiency and flexibility play a vital role. In this sense it is a systems programming language and early applications in the 1990s were in telecommunications, embedded systems, medical devices and Computer Aided Design (CAD) as well as first-generation option pricing risk management systems in computational finance. The rise in popularity continued well into the late 1990s as major vendors such as Microsoft, Sun and IBM began to endorse object-oriented technology in general and C++ in particular. It was also in this period that the Java programming language appeared which in time became a competitor to C++.

C++ remains one of the most important programming languages at the moment of writing. It is evolving to support new hardware such as multicore processors, GPUs (graphics processing units) and heterogeneous computing environments. It also has a number of mathematical libraries that are useful in computational finance applications.

1.3 C++ As a Multiparadigm Programming Language

We give an overview of the programming paradigms that C++ supports. In general, a programming paradigm is a way to classify programming languages according to the style of computer programming. Features of various programming languages determine which programming paradigms they belong to. C++ is a multiparadigm programming language because it supports the following styles:

• Procedural: organises code around functions, as typically seen in programs written in C, FORTRAN and COBOL. The style is based on structured programming in which a function or program is decomposed into simpler functions.
• Object-oriented: organises code around classes. A class is an abstract entity that encapsulates functions and data into a logical unit. We instantiate a class to produce objects. Furthermore, classes can be grouped into hierarchies. It is probably safe to say that this style is the most popular one in the C++ community.
• Generic/template: templates are a feature of C++ that allow functions and classes to operate with generic types. A function or class can then work on different data types.
• Functional: treats computation as the evaluation of mathematical functions. It is a declarative programming paradigm; this means that programming is done with expressions and declarations instead of statements. The output value of a function depends only on its input arguments.

The generic programming style is becoming more important and pronounced in C++, possibly at the expense of the traditional object-oriented model which is based on class hierarchies and subtype (dynamic) polymorphism. Template code tends to perform better at run-time while many errors are caught at compile-time, in contrast to object-oriented code where the errors tend to be caught by the linker or even at run-time.

The most recent style that C++ has (some) support for is functional programming. This style predates both structured and object-oriented programming. Functional programming has its origins in lambda calculus, a formal system developed by Alonzo Church in the 1930s to investigate computability, function definition, function application and recursion. Many functional programming languages can be viewed as elaborations on the lambda calculus. C++ supports the notion of lambda functions. A lambda function in C++ is an unnamed function but it has all the characteristics of a normal function. Here is an example of defining a stored lambda function (which we can define in place in code) and we then call it as a normal function:

In this case we see that the lambda function has a formal input string argument and it uses a captured variable cVar. Lambda functions are simple but powerful and we shall show how they can be used in computational finance.

C++11 is a major improvement on C++03 and it has a number of features that facilitate the design of software systems based on a combination of Structured Analysis and object-oriented technology. In general, we have a defined process to decompose a system into loosely coupled subsystems (Duffy, 2004). We then implement each subsystem in C++11. We discuss this process in detail in this book.

1.4 The Structure and Contents of this Book: Overview

This book examines C++ from a number of perspectives. In this sense it differs from other C++ literature because it discusses the full software lifecycle, starting with the problem description and eventually producing a working C++ program. In this book the topics are based on numerical analysis and its applications to computational finance (in particular, option pricing). In order to design and implement maintainable and efficient software systems we discuss each of the following building blocks in detail:

• A1: The new and improved syntax and language features in C++.
• A2: Integrating object-oriented, generic and functional programming styles in C++ code.
• A3: Replacing and upgrading the traditional Gang-of-Four software design patterns to fit into a multiparadigm design methodology.
• A4: Analysing and designing large and complex software systems using a combination of top-down system decomposition and bottom-up object assembly.
• A5: When writing applications, determining how much of the features in A1, A2, A3 and A4 to use.

The chapters can be categorised into those that deal with modern C++ syntax and language features, those that focus on system design and finally those chapters that discuss applications. In general, the first ten chapters introduce new language features. Chapters 11 to 19 focus on using C++ to create numerical libraries, visualisation software in Excel and lattice option pricing code. Chapters 20 to 29 are devoted to the finite difference method on the one hand and to multithreading and parallel processing on the other hand. The last three chapters of the book deal with Monte Carlo methods. For easy reference, we give a one-line summary of each chapter in the book:

1. Smart pointers, move semantics, r-value references.
2. All...