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.

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F# for Quantitative Finance
Johan Astborg
Dec, 2013 | 286 pages
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Table of Contents (17 chapters)
F# for Quantitative Finance
F# for Quantitative Finance
Credits
Credits
About the Author
About the Author
About the Reviewers
About the Reviewers
www.PacktPub.com
www.PacktPub.com
Preface
Preface
Free Chapter
1
Introducing F# Using Visual Studio
Introducing F# Using Visual Studio
Introduction
Getting started with Visual Studio
Understanding F# Interactive
Language overview
Explaining mutability and immutability
Primitive types
Explaining type inference
Explaining functions
Documenting your code
Your first application
The whole program
The power of prototyping
Functional languages in quantitative finance
Understanding the imperative code and interoperability
Summary
2
Learning More About F#
Learning More About F#
Structuring your F# program
Looking deeper inside data structures
Choosing data structures
More on functional programming
Asynchronous and parallel programming
A brief look at imperative programming
Using XML documentation
Summary
3
Financial Mathematics and Numerical Analysis
Financial Mathematics and Numerical Analysis
Understanding the number representation
Learning about numerical types in F#
Arithmetic operators
Learning about arithmetic comparisons
Math operators
Conversion functions
Introducing statistics
Using the Math.NET library
Learning about root-finding algorithms
Summary
4
Getting Started with Data Visualization
Getting Started with Data Visualization
Making your first GUI in F#
Composing interfaces
Displaying data
Extending the application to use Bollinger bands
Using FSharp.Charting
Creating a bar chart
Summary
5
Learning Option Pricing
Learning Option Pricing
Introduction to options
Learning the Black-Scholes formula
The Monte Carlo method
Summary
6
Exploring Volatility
Exploring Volatility
Introduction to volatility
Learning about implied volatility
Solving for implied volatility
Delta hedging using Black-Scholes
Exploring the volatility smile
Summary
7
Getting Started with Order Types and Market Data
Getting Started with Order Types and Market Data
Introducing orders
Understanding order execution
Introducing market data
Implementing simple pretrade risk analysis
Introducing FIX and QuickFIX/N
Summary
8
Setting Up the Trading System Project
Setting Up the Trading System Project
Explaining automated trading
Understanding software testing and test-driven development
Understanding NUnit and FsUnit
Connecting to Microsoft SQL Server
Introducing type providers
Writing test cases
Summary
9
Trading Volatility for Profit
Trading Volatility for Profit
Trading the volatility
Plotting payoff diagrams with FSharpCharts
Learning directional trading strategies
Deriving the mathematics
Learning relative value trading strategies
Defining the trading strategy
Summary
10
Putting the Pieces Together
Putting the Pieces Together
Understanding the requirements
Revisiting the structure of the system
Understanding the Model-View-Controller pattern
Executing the trading strategy using a framework
Building the GUI
Presenting information in the GUI
Adding support for downloading the data
Looking at possible additions to the system
Summary
Index
Index

Deriving the mathematics

In this section, we'll look at the mathematics needed to trade a delta neutral portfolio.

The following table presents values of a market neutral portfolio:

The following table shows the values of the market neutral portfolio for the next day:

Hedging with implied volatility

In this section, we are going to derive the mathematical tools for hedging with implied volatility to be able to watch the mark to market profit and loss.

The following is the mark to market profit from the current day to the next day:

Here, S is the stock price and Γ is the Black-Scholes gamma function.

The following is the theoretical profit until the end of the arbitrage trade:

We integrate the discounted value of each profit made until the end of the trade to get the total theoretical profit.

Implementing the mathematics

Using Math.NET, let's implement the mathematics derived in the previous section to get a feel of the close connection between the formulas and F#:

/// Mark-to-market profit

/// Normal...
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