**by Bernt Arne Ødegaard**

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This book is a a discussion of the calculation of specific formulas in finance. The field of finance has seen a rapid development in recent years, with increasing mathematical sophistication. While the formalization of the field can be traced back to the work of Markowitz (1952) on investors mean-variance decisions and Modigliani and Miller (1958) on the capital structure problem, it was the solution for the price of a call option by Black and Scholes (1973); Merton (1973) which really was the starting point for the mathematicalization of finance. The fields of derivatives and fixed income have since then been the main fields where complicated formulas are used. This book is intended to be of use for people who want to both understand and use these formulas, which explains why most of the algorithms presented later are derivatives prices.

This project started when I was teaching a course in derivatives at the University of British Columbia, in the course of which I sat down and wrote code for calculating the formulas I was teaching. I have always found that implementation helps understanding these things. For teaching such complicated material it is often useful to actually look at the implementation of how the calculation is done in practice. The purpose of the book is therefore primarily pedagogical, although I believe all the routines presented are correct and reasonably efficient, and I know they are also used by people to price real options.

To implement the algorithms in a computer language I choose C++. My students keep asking why anybody would want to use such a backwoods computer language, they think a spreadsheet can solve all the worlds problems. I have some experience with alternative systems for computing, and no matter what, in the end you end up being frustrated with higher end "languages", such as Matlab og R (Not to mention the straitjacket which is is a spreadsheet.) and going back to implementation in a standard language. In my experience with empirical finance I have come to realize that nothing beats knowledge a real computer language. This used to be FORTRAN, then C, and now it is C++. All example algorithms are therefore coded in C++. I do acknowledge that matrix tools like Matlab are very good for rapid prototyping and compact calculations, and will in addition to C++ in places also illustrate the use of Matlab, as well as other (public domain) tools. ### Table of Contents

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This project started when I was teaching a course in derivatives at the University of British Columbia, in the course of which I sat down and wrote code for calculating the formulas I was teaching. I have always found that implementation helps understanding these things. For teaching such complicated material it is often useful to actually look at the implementation of how the calculation is done in practice. The purpose of the book is therefore primarily pedagogical, although I believe all the routines presented are correct and reasonably efficient, and I know they are also used by people to price real options.

To implement the algorithms in a computer language I choose C++. My students keep asking why anybody would want to use such a backwoods computer language, they think a spreadsheet can solve all the worlds problems. I have some experience with alternative systems for computing, and no matter what, in the end you end up being frustrated with higher end "languages", such as Matlab og R (Not to mention the straitjacket which is is a spreadsheet.) and going back to implementation in a standard language. In my experience with empirical finance I have come to realize that nothing beats knowledge a real computer language. This used to be FORTRAN, then C, and now it is C++. All example algorithms are therefore coded in C++. I do acknowledge that matrix tools like Matlab are very good for rapid prototyping and compact calculations, and will in addition to C++ in places also illustrate the use of Matlab, as well as other (public domain) tools.

This open book is licensed under a Open Publication License (OPL). You can download Financial Numerical Recipes in C++ ebook for free in PDF format (1.4 MB).

Chapter 1

On C++ and programming

Chapter 2

Matrix Tools

Chapter 3

The value of time

Chapter 4

Bond Pricing with a flat term structure

Chapter 5

The term structure of interest rates and an object lesson

Chapter 6

The Mean Variance Frontier

Chapter 7

Futures algoritms

Chapter 8

Binomial option pricing

Chapter 9

Basic Option Pricing, the Black Scholes formula

Chapter 10

Warrants

Chapter 11

Extending the Black Scholes formula

Chapter 12

Option pricing with binomial approximations

Chapter 13

Finite Differences

Chapter 14

Option pricing by simulation

Chapter 15

Pricing American Options - Approximations

Chapter 16

Average, lookback and other exotic options

Chapter 17

Generic binomial pricing

Chapter 18

Trinomial trees

Chapter 19

Alternatives to the Black Scholes type option formula

Chapter 20

Pricing of bond options, basic models

Chapter 21

Credit risk

Chapter 22

Term Structure Models

Chapter 23

Binomial Term Structure models

Chapter 24

Interest rate trees

Chapter 25

Building term structure trees using the Ho and Lee (1986) approach

Chapter 26

Term Structure Derivatives

Chapter 27

Date (and time) revisited - the BOOST libraries

Title

Financial Numerical Recipes in C++

Subject

Computer Science

Publisher

Self-publishing

Published

2014

Pages

264

Edition

1

Language

English

PDF Size

1.4 MB

License

Open Publication License

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