Financial Instrument Pricing Using C++

One of the best languages for the development of financial engineering and instrument pricing applications is C++. It has several features that allow developers to write robust, flexible and extensible software systems. It is an ANSI/ISO standard, fully object–oriented and interfaces with many third–party applications. It has support for templates and generic programming, massive reusability using templates (‘write once’) and support for legacy C applications.
In this book we bring C++ to the next level by applying it to the design and implementation of classes, libraries and applications for option and derivative pricing models. We employ modern software engineering techniques to produce industrial–strength applications: –Using the Standard Template Library (STL) in financeCreating your own template classes and functionsReusable data structures for vectors, matrices and tensorsClasses for numerical analysis (numerical linear algebra …)Solving the Black Scholes equations, exact and approximate solutionsImplementing the Finite Difference Method in C++Integration with the ‘Gang of Four’ Design PatternsInterfacing with Excel (output and Add–Ins)Financial engineering and XMLCash flow and yield curves
Included with the book is a CD containing the source code in the Datasim Financial Toolkit that you can use directly. This will get you up to speed with your C++ applications by reusing existing classes and libraries.
′Unique... Let′s all give a warm welcome to modern pricing tools.′ Paul Wilmott, mathematician, author and fund manager

Spis treści:
1 Executive Overview of this Book.
1.1 What is this book?
1.2 What’s special about this book?
1.3 Who is this book for?
1.4 Software requirements.
1.5 The structure of this book.
1.6 Pedagogical approach.
1.7 What this book is not.1.8 Source code on the CD.
PART I TEMPLATE PROGRAMMING IN C++.
2 A Gentle Introduction to Templates in C++.
2.1 Introduction and objectives.
2.2 Motivation and background.
2.3 Defining a template.
2.3.1 An example.
2.4 Template instantiation.
2.5 Function templates.
2.5.1 An example.
2.6 Default values and typedefs.
2.7 Guidelines when implementing templates.
2.8 Conclusions and summary.
3 An Introduction to the Standard Template Library.
3.1 Introduction and objectives.
3.1.1 Why use STL?
3.2 A Bird’s–eye view of STL.
3.3 Sequence containers.
3.3.1 Programming lists.
3.3.2 Vectors and arrays in STL.
3.4 Associative containers.
3.4.1 Sets in STL.
3.4.2 Maps in STL.
3.5 Iterators in STL.
3.5.1 What kinds of iterators?
3.6 Algorithms.
3.7 Using STL for financial instruments.
3.8 Conclusions and summary.
4 STL for Financial Engineering Applications.
4.1 Introduction and objectives.
4.2 Clever data structures.
4.2.1 A simple output mechanism.
4.3 Set theory and STL.
4.4 Useful algorithms.
4.5 STL adaptor containers.
4.6 Conclusions and summary.
5 The Property Pattern in Financial Engineering.
5.1 Introduction and objectives.
5.2 The Property pattern.
5.2.1 Requirements for a Property pattern.
5.3 An example.
5.4 Extending the Property pattern: property sets and property lists.
5.4.1 An example.
5.5 Properties and exotic options.
5.5.1 Example: Executive options.
5.6 Conclusions and summary.
PART II BUILDING BLOCK CLASSES.
6 Arrays, Vectors and Matrices.
6.1 Introduction and objectives.
6.2 Motivation and background.
6.3 A layered approach.
6.4 The Array and Matrix classes in detail.
6.4.1 Simple print functions.
6.4.2 Array example.
6.4.3 Matrix example.
6.5 The Vector and NumericMatrix classes in detail.
6.5.1 Vector example.
6.5.2 Numeri cMatrix example.
6.6 Associative arrays and matrices.
6.7 Conclusions and summary.
7 Arrays and Matrix Properties.
7.1 Introduction and objectives.
7.2 An overview of the functionality.
7.3 Software requirements.
7.3.1 Accuracy.
7.3.2 Efficiency.
7.3.3 Reliability.
7.3.4 Understandability.
7.4 The core processes.
7.4.1 Interactions between matrices and vectors.
7.4.2 Some examples.
7.5 Other function categories.
7.5.1 Measures of central tendency.
7.5.2 Measures of dispersion.
7.5.3 Moments, skewness, kurtosis.
7.5.4 Inequalities.
7.6 Using the functions.
7.6.1 Calculating historical volatility.
7.6.2 Variance of return of a portfolio.
7.7 An introduction to exception handling.
7.7.1 Try, throw and catch: A bit like tennis.
7.8 Conclusions and summary.
8 Numerical Linear Algebra.
8.1 Introduction and objectives.
8.2 An introduction to numerical linear algebra.
8.2.1 Direct methods.
8.2.2 Iterative methods.
8.3 Tridiagonal systems.
8.3.1 LU decomposition.
8.3.2 Godunov’s Double Sweep method.
8.3.3 Designing and implementing tridiagonal schemes.
8.4 Block tridiagonal systems.
8.5 What requirements should our matrix satisfy?
8.5.1 Positive–definite matrices and diagonal dominance.
8.5.2 M–Matrices.
8.6 Conclusions and summary.
9 Modelling Functions in C++.
9.1 Introduction and objectives.
9.2 Function pointers in C++.
9.3 Function objects in STL.
9.3.1 Comparison functions.
9.3.2 STL and financial engineering.
9.4 Some function types.
9.4.1 Applications in numerical analysis and financial engineering.
9.4.2 An example: Functions in option pricing.
9.5 Creating your own function classes.
9.6 Arrays of functions.
9.7 Vector functions.
9.8 Real–valued functions.
9.9 Vector–valued functions.
9.10 Conclusions and summary.
10 C++ Classes for Statis tical Distributions.
10.1 Introduction and objectives.
10.2 Discrete and continuous probability distribution functions.
10.3 Continuous distributions.
10.3.1 Uniform (rectangular) distribution.
10.3.2 Normal distribution.
10.3.3 Lognormal distribution.
10.3.4 Gamma distribution and its specializations.
10.4 Discrete distributions.
10.4.1 Poisson distribution
10.4.2 Binomial and Bernoulli distributions.
10.4.3 Pascal and geometric distributions.
10.5 Tests.
10.5.1 Continuous distributions.
10.5.2 Discrete distributions.
10.6 Conclusions and summary.
PART III ORDINARY AND STOCHASTIC DIFFERENTIAL EQUATIONS.
11 Numerical Solution of Initial Value Problems: Fundamentals.
11.1 Introduction and objectives.
11.2 A model problem.
11.2.1 Qualitative properties of the solution.
11.3 Discretisation.
11.4 Common schemes.
11.5 Some theoretical issues.
11.6 Fitting: Special schemes for difficult problems.
11.7 Non–linear scalar problems and predictor–corrector methods.
11.8 Extrapolation techniques.
11.9 C++ design and implementation.
11.10 Generalisations.
11.11 Conclusions and summary.
12 Stochastic Processes and Stochastic Differential Equations.
12.1 Introduction and objectives.
12.2 Random variables and random processes.
12.2.1 Random variables.
12.2.2 Generating random variables.
12.2.3 Random (stochastic) processes.
12.3 An introduction to stochastic differential equations.
12.4 Some finite difference schemes.
12.4.1 Improving the accuracy: Richardson extrapolation.
12.5 Which scheme to use?
12.6 Systems of SDEs.
12.7 Conclusions and summary.
13 Two–Point Boundary Value Problems.
13.1 Introduction and objectives.
13.2 Description of problem.
13.3 (Traditional) centred–difference schemes.
13.3.1 Does the discrete system have a solution?
13.3.2 Extrapolation.
13.4 Approximation