Book Image

F# for Quantitative Finance

By : Johan Astborg
Book Image

F# for Quantitative Finance

By: Johan Astborg

Overview of this book

F# is a functional programming language that allows you to write simple code for complex problems. Currently, it is most commonly used in the financial sector. Quantitative finance makes heavy use of mathematics to model various parts of finance in the real world. If you are interested in using F# for your day-to-day work or research in quantitative finance, this book is a must-have.This book will cover everything you need to know about using functional programming for quantitative finance. Using a functional programming language will enable you to concentrate more on the problem itself rather than implementation details. Tutorials and snippets are summarized into an automated trading system throughout the book.This book will introduce you to F#, using Visual Studio, and provide examples with functional programming and finance combined. The book also covers topics such as downloading, visualizing and calculating statistics from data. F# is a first class programming language for the financial domain.
Table of Contents (17 chapters)
F# for Quantitative Finance
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Index

Learning about root-finding algorithms


In this section, we'll learn about the different methods used in numerical analysis to find the roots of functions. Root-finding algorithms are very useful, and we will learn more about their applications when we talk about volatility and implied volatility.

The bisection method

In this section, we will look at a method for finding the roots of a function using the bisection method. This method will be used later in this book to numerically find the implied volatility for an option that is given a certain market price. The bisection method uses iteration and repeatedly bisects an interval for the next iteration.

The following function implements bisection in F#:

let rec bisect n N (f:float -> float) (a:float) (b:float) (t:float) : float =
  if n >= N then -1.0
  else
    let c = (a + b) / 2.0
    if f(c) = 0.0 || (b - a) / 2.0 < t then
      // Solution found
      c
    else
      if sign(f(c)) = sign(f(a)) then
        bisect (n + 1) N f c b...