F# for Quantitative Finance

Table of Contents

F# for Quantitative Finance

Credits

About the Author

About the Reviewers

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Free Access for Packt account holders

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Downloading the example code

Errata

Piracy

Questions

1. Introducing F# Using Visual Studio

Introduction

Getting started with Visual Studio

Creating a new F# project

Creating a new project in Visual Studio

Understanding the program template

Adding an F# script file

Understanding F# Interactive

Language overview

Explaining mutability and immutability

Primitive types

Explaining type inference

Explaining functions

Learning about anonymous functions

Explaining higher-order functions

Currying

Investigating lists

Concatenating lists

Tuples

The pipe operator

Documenting your code

Your first application

The whole program

Understanding the program

Extending the example program

The entire program

The power of prototyping

Functional languages in quantitative finance

Understanding the imperative code and interoperability

Summary

2. Learning More About F#

Structuring your F# program

Looking into modules

Using functions and values in modules

Namespaces

Looking deeper inside data structures

Record types

Discriminated unions

Enumerations

Arrays

Interesting functions in an array module

Lists

Pattern matching and lists

Interesting functions in a list module

Sequences

Interesting functions in the sequence module

Sets

Maps

Interesting functions in the map module

Options

Strings

Interesting functions in the string module

Choosing data structures

Arrays

Lists

Sets

Maps

More on functional programming

Recursive functions

Tail recursion

Pattern matching

Incomplete pattern matching

Using guards

Pattern matching in assignment and input parameters

Active patterns

Introducing generics

Lazy evaluation

Units of measure

Asynchronous and parallel programming

Events

Background workers

Threads

Thread pools

Asynchronous programming

The F# asynchronous workflows

Asynchronous binding

Examples of using an async workflow

Parallel programming using TPL

MailboxProcessor

A brief look at imperative programming

Object-oriented programming

Classes

Objects and members

Methods and properties

Overloaded operators

Using XML documentation

Useful XML tags

Typical XML documentation

Summary

3. Financial Mathematics and Numerical Analysis

Understanding the number representation

Integers

Two's complement

Floating-point numbers

The IEEE 754 floating-point standard

Learning about numerical types in F#

Arithmetic operators

Learning about arithmetic comparisons

Math operators

Conversion functions

Introducing statistics

Aggregate statistics

Calculating the sum of a sequence

Calculating the average of a sequence

Calculating the minimum of a sequence

Calculating the maximum of a sequence

Calculating the variance and standard deviation of a sequence

Calculating variance

Calculating standard deviation

Looking at an example application

Using the Math.NET library

Installing the Math.NET library

Introduction to random number generation

Pseudo-random numbers

Mersenne Twister

Probability distributions

Normal distribution

Statistics

Linear regression

Using the least squares method

Using polynomial regression

Learning about root-finding algorithms

The bisection method

Looking at an example

Finding roots using the Newton–Raphson method

Looking at an example

Finding roots using the secant method

Looking at an example

Summary

4. Getting Started with Data Visualization

Making your first GUI in F#

Composing interfaces

More about agents

The user interface

The main application

Learning about event handling

Displaying data

Extending the form to use a table

Displaying financial data from Yahoo! Finance

Understanding the application code

Extending the application to use Bollinger bands

Using FSharp.Charting

Creating a candlestick chart from stock prices

Creating a bar chart

Summary

5. Learning Option Pricing

Introduction to options

Looking into contract specifications

European options

American options

Exotic options

Learning about Wiener processes

Learning the Black-Scholes formula

Implementing Black-Scholes in F#

Using Black-Scholes together with charts

Introducing the greeks

First-order greeks

Second-order greeks

Implementing the greeks in F#

Delta

Gamma

Vega

Theta

Rho

Investigating the sensitivity of the greeks

Code listing for visualizing the four greeks

The Monte Carlo method

Summary

6. Exploring Volatility

Introduction to volatility

Actual volatility

Implied volatility

Exploring volatility in F#

The complete application

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

Introducing orders

Order types

Market orders

Limit orders

Conditional and stop-orders

Order properties

Understanding order execution

Introducing market data

Implementing simple pretrade risk analysis

Validating orders

Introducing FIX and QuickFIX/N

Using FIX 4.2

Configuring QuickFIX to use the simulator

Summary

8. Setting Up the Trading System Project

Explaining automated trading

Understanding software testing and test-driven development

Understanding NUnit and FsUnit

Requirements for the system

Setting up the project

Installing the NUnit and FsUnit frameworks

Connecting to Microsoft SQL Server

Introducing type providers

Using LINQ and F#

Explaining sample code using type providers and LINQ

Creating the remaining table for our project

Writing test cases

Details about the setup

Summary

9. Trading Volatility for Profit

Trading the volatility

Plotting payoff diagrams with FSharpCharts

Learning directional trading strategies

Trading volatility using options

Trading the straddle

Long straddle

Short straddle

Trading the butterfly spread

The long butterfly spread

The short butterfly spread

Trading the VIX

Trading the delta neutral portfolio

Deriving the mathematics

Hedging with implied volatility

Implementing the mathematics

Learning relative value trading strategies

Trading the slope of the smile

Defining the trading strategy

Case 1 – increasing the slope

Case 2 – decreasing the slope

Defining the entry rules

Defining the exit rules

Summary

10. Putting the Pieces Together

Understanding the requirements

Revisiting the structure of the system

Understanding the Model-View-Controller pattern

The model

The view

The controller

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

Improving the data feed

Support for backtesting

Extending the GUI

Converting to the client-server architecture

Summary

Index

F# for Quantitative Finance

F# for Quantitative Finance

Copyright © 2013 Packt Publishing

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First published: December 2013

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Credits

Author

Johan Astborg

Reviewers

Yan Cui

Arthur Pham

Isaac Abraham

Acquisition Editors

Sam Birch

Aarthi Kumaraswamy

Kunal Parikh

Lead Technical Editor

Athira Laji

Copy Editors

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Shambhavi Pai

Technical Editors

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Project Coordinator

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Proofreader

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Indexers

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Mariammal Chettiyar

Tejal Soni

Graphics

Ronak Dhruv

Production Coordinator

Melwyn D'sa

Cover Work

Melwyn D'sa

About the Author

Johan Astborg is the developer and architect of various kinds of software systems and applications, financial software systems, trading systems, as well as mobile and web applications. He is interested in computer science, mathematics, and quantitative finance, with a special focus on functional programming. Johan is passionate about languages such as F#, Clojure, and Haskell, and operating systems such as Linux, Mac OS X, and Windows for his work. Most of Johan's quantitative background comes from Lund University, where he studied courses in computer science, mathematics, and physics. Currently Johan is studying pure mathematics at Lund University, Sweden, and is aiming for a PhD in the future, combining mathematics and functional programming. Professionally, Johan has worked as a part-time developer for Sony Ericsson and various smaller firms in Sweden. He also works as a part-time consultant focusing on web technologies and cloud solutions. You can easily contact him by sending an e-mail to <[email protected]> or visit his GitHub page at https://github.com/joastbg.

About the Reviewers

Yan Cui (@theburningmonk) is a lead server-side developer at the London-based, award winning gaming company GameSys. He focuses on building highly distributed and scalable server-side solutions for GameSys's social and mobile games. Yan is a regular speaker on topics such as F#, AOP, and NoSQL at local user groups and conferences in the UK and keeps an active blog at http://theburningmonk.com. He is also a co-author of the upcoming book, F# Deep Dives, Manning Publications.

Arthur Pham is working for for Thomson Reuters as a Lead Quantitative Engineer since 2006. He has spent many years designing and implementing derivatives pricing models and still loves learning new programming languages like F#, C++, Python, Flex/Actionscript, C#, Ruby, and JavaScript.

He currently lives in New York, USA, and can be contacted on Twitter @arthurpham.

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Preface

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 the real world. If you are interested in using F# for your day-to-day work or research in quantitative finance, this book is for you.

This book covers everything you need to know about using functional programming for quantitative finance. Using a functional programming language for quantitative finance will enable you to concentrate more on the model itself rather than the implementation details. Tutorials and snippets are summarized into a trading system throughout this book.

F#, together with .NET, provides a wide range of tools needed to produce high quality and efficient code, from prototyping to production. The example code snippets in this book can be extended into larger blocks of code, and reused and tested easily in a functional language. F# is considered one of the default functional languages of choice for financial and trading-related applications.

What this book covers

Chapter 1, Introducing F# Using Visual Studio, introduces you to F# and its roots in functional languages. You will learn how to use F# in Visual Studio and write your first application.

Chapter 2, Learning More About F#, teaches you more about F# as a language and illustrates the many sides of this paradigm language.

Chapter 3, Financial Mathematics and Numerical Analysis, introduces the toolset we'll need throughout the book to implement financial models and algorithms.

Chapter 4, Getting Started with Data Visualization, introduces some of the most common ways to use F# to visualize data and display information in a GUI.

Chapter 5, Learning Option Pricing, teaches you about options, the Black-Scholes formula and ways of exploring options using the tools at hand.

Chapter 6, Exploring Volatility, digs deeper into the world of Black-Scholes and teaches you about implied volatility.

Chapter 7, Getting Started with Order Types and Market Data, takes a rather pragmatic approach towards finance and implements a basic order management system.

Chapter 8, Setting Up the Trading System Project, builds the foundation for the project and shows how to connect to SQL Server and use LINQ for queries.

Chapter 9, Trading Volatility for Profit, studies various ways of monetizing through movements in volatility and the arbitrage opportunity defining the trading strategy for the project.

Chapter 10, Putting the Pieces Together, shows the final steps towards the complete trading system using a volatility arbitrage strategy and FIX 4.2.

What you need for this book

Apart from an interest in F# and finance, you need a computer with Visual Studio 2012 installed. Visual Studio 2012 is the recommended IDE, supporting F# 3.0.

Who this book is for

This book is for anyone interested in writing F# code in the financial domain, with a quantitative approach. The book is mainly intended to be a source of inspiration and uses a lot of working code examples to illustrate both the concepts of finance and F# as a functional language.

At the end of the book we develop a simple trading system for volatility arbitrage. Details about orders and the FIX protocol are explained, as well as the theory behind the strategy itself. This may work as a foundation for anyone interested in developing their own trading system based on options and volatility.

Conventions

In this book, you will find a number of styles of text that distinguish between different kinds of information. Here are some examples of these styles, and an explanation of their meaning.

Code words in text, database table names, folder names, filenames, file extensions, pathnames, dummy URLs, user input are shown as follows: First we set a flag in the constructor, WorkerSupportsCancellation = true, then we check a flag every time we iterate the calculation.

A block of code is set as follows:

let rec getSecondLastElement = function

        | head :: tail :: [] -> head

        | head :: tail -> getSecondLastElement tail

When we wish to draw your attention to a particular part of a code block, the relevant lines or items are set in bold:

SocketConnectPort=9878 SocketConnectHost=192.168.0.25

FileStorePath=temp

New terms and important words are shown in bold. Words that you see on the screen, in menus or dialog boxes for example, appear in the text like this: If you run this code, you will see a form with the title Displaying data in F#, like the one in the following screenshot.

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Downloading the example code

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Questions

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Chapter 1. Introducing F# Using Visual Studio

In this chapter, you will learn about the history of F# and its roots in other programming languages. We will also be introducing Visual Studio and the fundamental language constructs of F#. You will be comfortable using the interactive mode for prototyping the code step-by-step. You will get a better understanding of how to build programs in F# by putting pieces together. Also, the basics of the language are covered by using and evaluating the code in the Read Eval Print Loop (REPL).

In this chapter you will learn:

How to use F# with Visual Studio 2012

How to use F# Interactive to write the code in a new exploratory way

The basics of F# and how to write your first non-toy application

How functional programming will make you more productive

Introduction

Before we dive in to the language itself, we should discuss why we need it in the first place. F# is a powerful language, which may sound like a cliché, but it combines multiple paradigms into real-life productivity and supports the .NET components and libraries natively as well as the Common Language Infrastructure (CLI). Functional programming has long been associated with academics and experts. F# is one of the few languages offering a complete environment that is mature enough to comfortably be integrated into an organization.

Also, F# has extensive support for parallel programming, where advanced features such as asynchronous and multi-threaded concepts are implemented as language constructs. It hides a lot of implementation details from the programmer. In F#, the functional programming