F# for Quantitative Finance

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 paradigm is the main philosophy used to solve problems. The other paradigms, object-oriented and imperative programming, are prioritized to be used as subsidiaries and complements for this main paradigm. Reasons for them to coexist, involves compatibility and pragmatic, real-world productivity concerns.

We will start by introducing Visual Studio as the main tool of choice for this book. Although it's possible to use the standalone F# compiler and your favorite editor, you will most likely be more productive using Visual Studio 2012, as we will do throughout this book.

F# has been a part of Visual Studio since 2010. We will use the latest version of Visual Studio and F# throughout this book. This will enable us to use the latest functionality and enhancements available in Visual Studio 2012 and F# 3.0.

F# is open source, which means you can use it on any supported platform; it's not bound to Microsoft or Visual Studio. There is good support in other IDEs, such as MonoDevelop, which will run on Linux and Mac OS X.

Creating a new F# project

Create a new project in Visual Studio for F#, which is to be used in this guide to explore the basics, as shown in the following sections.

Creating a new project in Visual Studio

Using the following steps, we can create a new project in Visual Studio:

1. To create your first F# project, open Visual Studio 12 and navigate to File | New | Project, then, from the menu select New Project.

   

2. Now you will see the New Project window appear. Select F# in the left panel and then select F# Application. You can name it anything you like. Finally, click on OK.

   

3. Now you have created your first F# application, which will just print the arguments passed to it.

Understanding the program template

Let's have a brief look at the program template generated by Visual Studio.

If you run this program, which will just print out the arguments passed to it, you will see a terminal window appear.

The [<EntryPoint>] function in the preceding screenshot is the main function, which tells Visual Studio to use that particular function as the entry point for the program executable. We will not dig any deeper into this program template for now, but we will come back to this in the last three chapters when we'll build the trading system.

Adding an F# script file

We will use an F# script file after having looked at the standard program template instead of exploring the basics of the language in a more interactive fashion. You can think of F# script files as notebooks, where you have executable code that you can explore in pieces in an incremental style:

1. Add the F# script file by right-clicking on the Solution Explorer to the right of the code editor.

2. Then navigate to Add | New Item…, as shown in the following screenshot:

   

3. You can name the script file anything you like, such as GettingStarted.fsx.

   

Now that we have set up the basic project structure in Visual Studio, let's continue and explore F# Interactive.

F# Interactive is a way of executing parts of a program interactively. Doing this enables you as a programmer to explore parts of the code and how it behaves. You will have a more dynamic feel for writing code. It's also more fun. F# Interactive is a REPL for F#. This means, it will read the code, evaluate it, and then print out the result. It will then do this over and over again. It's much like a command line, where the code is executed and the result is displayed to the user.

To execute a code in F# Interactive, have a look at the following steps:

We will now start our journey into functional programming using F#, and explore its capabilities in quantitative finance applications.

Let's start by looking at how values are declared, that is, how to bind values to names, mutability, and immutability.

To initialize and create a value, use the let keyword. let will bind the value on the right-hand side to the variable name on the left-hand side of the equals sign. This is a bind operator, a lot like math.

let sum = 4 + 5
let newsum = sum + 3

The let binding is also used in the same way for binding functions to a name, as we will see in the following sections.

Once a variable is defined to have a particular value, it keeps that value indefinitely. There are exceptions to this, and shadowing can be used to override a previous assignment made within the same scope. Thus, variables in mathematics are immutable. Similarly, variables in F# are immutable with some exceptions.

Immutable variables are default in F#. They are useful because they are thread-safe and easier to reason about. This is one of the reasons you may have heard a lot about immutability recently. The concept is to solve the biggest issues and design flaws of concurrent programming, including shared mutable state. If the values do not change, there is no need to protect them either, which is one of the reasons for promoting immutability in concurrent programming.

If you try to alter the value of an immutable variable, you will encounter a message similar to the following:

let immutable = "I am immutable!"
immutable <- "Try to change it..."
… error FS0027: This value is not mutable

Sometimes, however, it's desirable to have variables that are mutable. Often the need arises in real-life applications when some global state is shared like a counter. Also, object-oriented programming and interoperability with other .NET languages makes the use of mutability unavoidable.

To create a mutable variable, you simply put the keyword mutable in front of the name as shown in the following line of code:

let mutable name = firstname + lastname

To change the variable, after it is created, use the arrow operator (←) as shown in the following line of code:

name ← "John Johnson"

This is a little bit different from other languages. But once you have wrapped your head around the concept, it makes more sense. In fact, it will most likely be one of the main ways to reason about variables in the future as well.

It may look like F# is a dynamic typed language like JavaScript, Ruby, or Python. In fact, F# is statically typed like C#, C++, and Java. It uses type inference to figure out the correct types. Type inference is a technique which is used to automatically deduce the type used by analyzing the code. This approach works remarkably well in nearly all situations. However, there are circumstances in which you as a programmer need to make clarifications to the compiler. This is done using type annotations, a concept we will look into in the following sections.

Let's explore some of the built-in types in F# using the REPL.

> let anInt = 124;;

val anInt : int = 124

This means that F# figured out the type of anInt to be of type int. It simply inferred the type on the left-hand side to be of the same type as the right-hand side of the assignment. Logically, the type must be the same on both sides of the assignment operator, right?

We can extend our analysis into floating point numbers as shown in the following lines of code:

> let anFloat = 124.00;;

val anFloat : float = 124.0

Because of the decimal sign, the type is determined to be of type float. The same holds true for double as shown in the following lines of code:

> let anDouble : double = 1.23e10;;

val anDouble : double = 1.23e+10

For other types, it works in the same way as expected as shown in the following:

> let myString = "This is a string";;

val myString : string = "This is a string"

All the primitive built-in types, except for unit, have a corresponding type in .NET.

The following table shows the most common primitive types in F#:

There are also other types that are built into the language which will be covered in more detail in the next chapter, such as lists, arrays, sequences, records, and discriminated unions.

Type inference means that the compiler will automatically deduce the type of an expression used in the code, based on the information provided from the programmer about the context of the expression. Type inference analyses the code, as you have seen in the preceding section, to determine types that are often obvious to the programmer. This spares the programmer from having to explicitly define the types of every single variable. It's not always needed to have the types defined to be able to understand the code, as seen in the preceding section for simple assignments of integers and floats. Type inference will make the code easier to write, and as a consequence, easier to read, leaving a lot of ceremony where it belongs.

It's now time to look at functions, the most basic and powerful building block in F#, and any other functional programming language for that matter. Functional programming languages use functions as first class constructs, in contrast to object-oriented programming, where objects and data are first class constructs. This means that in functional programming, functions will produce data based on the input and not based on state. In object-oriented programming, the state is encapsulated into objects and passed around. Functions are declared in the same way as variables were declared previously in the preceding snippets, with let bindings. Have a look at the following code snippet:

let sum (x,y) =
	x + y
> sum (7, 7)

If you try to evaluate the first sum function using Alt + Enter, F# Interactive will respond with a function like the following line of code:

val sum : x:int -> y:int -> int

This means that sum is a function that takes two values of type int and returns a value of type int. The compiler simply knows that it's just the last type that is the return type.

let sum (x:float, y:float) =
	x + y

> sum(7.0, 7.0);;
val it : float = 14.0

Let's look at the following case where parameters of wrong types are passed to the function:

> sum(7, 7);;
...
error FS0001: This expression was expected to have type float
but here has type int

As seen in the modified version of the sum function, the types are explicitly declared as float. This is a way of telling the compiler beforehand that float is the value to be used in the function. The first version of sum used type inference to calculate the types for x and y respectively and found it to be of type int.

let square = (fun x → x * x)
> square 2
val it : int = 4

let squareByFour f
	f 4
> squareByFour square

let sum x y =
	x + y

sum 2 3
sum 2 4
sum 2 5

let sumBy2 y = 
	sum 2 y

> sumBy2 3;;
val it : int = 5

> sumBy2 4;;
val it : int = 5

> sumBy2 5;;
val it : int = 5

Investigating lists

Lists in F# are very useful, they are some of the most frequently used building blocks. They are the basic building blocks in functional languages and often replace the need of other types or classes. This is because the support for manipulating and creating lists and also being able to nest lists can be enough to replace custom types. You can think of lists as a sequence of values of the same type.

Lists in F# are the following:

• A powerful way to store data

• Immutable linked lists of values of any type

• Often used as building blocks

• One of the best ways to store data

This illustrates a list in F#, with a head and a tail, where each element is linked to the next.

Let's consider the following simple list of price information which are represented as floating points:

let prices = [45.0; 45.1; 44.9; 46.0]
> val prices : float list = [45.0; 45.1; 44.9; 46.0]

Suppose you want a list with values between 0 and 100, instead of writing them yourself, F# can do it for you. Take a look at the following lines of code:

let range = [0 .. 100]
val range : int list =
  [0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17;
  18; 19; 20;21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32;
  33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47;
  48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62;
  63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77;
  78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 
  93; 94; 95; 96; 97; 98; 99; ...]

This is fine if we just want a simple range with fixed size increments. Sometimes however, you may want to have a smaller increment, let's say 0.1, which is between 1.0 and 10.0. The following code shows how it is done:

let fineRange = [1.0 .. 0.1 .. 10.0]
val fineRange : float list =
[1.0; 1.1; 1.2; 1.3; 1.4; 1.5; 1.6; 1.7; 1.8; 1.9; 2.0; 2.1; 2.2; 2.3; 2.4; 2.5; 2.6; 2.7; 2.8; 2.9; 3.0; 3.1; 3.2; 3.3; 3.4; 3.5; 3.6; 3.7; 3.8; 3.9; 4.0; 4.1; 4.2; 4.3; 4.4; 4.5; 4.6; 4.7; 4.8; 4.9; 5.0; 5.1; 5.2; 5.3; 5.4; 5.5; 5.6; 5.7; 5.8; 5.9; 6.0; 6.1; 6.2; 6.3; 6.4; 6.5; 6.6; 6.7; 6.8; 6.9; 7.0; 7.1; 7.2; 7.3; 7.4; 7.5; 7.6; 7.7; 7.8; 7.9; 8.0; 8.1; 8.2; 8.3; 8.4; 8.5; 8.6; 8.7; 8.8; 8.9; 9.0; 9.1; 9.2; 9.3; 9.4; 9.5; 9.6; 9.7; 9.8; 9.9; 10.0]

Lists can be of any type, and type inference works here as well. Have a look at the following code:

> let myList = ["One"; "Two"; "Three"];;
val myList : string list = ["One"; "Two"; "Three"]

However, if you mix the types in a list, the compiler will get confused about the actual type used:

let myList = ["One"; "Two"; 3.0];; 
...
This expression was expected to have type
string but here has type float 

Tip

Downloading the example code

You can download the example code files for all Packt books you have purchased from your account at http://www.packtpub.com. If you purchased this book elsewhere, you can visit http://www.packtpub.com/support and register to have the files e-mailed directly to you.

Concatenating lists

Concatenating lists is useful when you want to add lists together. This is done using the @ operator. Have a look at the following code where the @ operator is used:

> let myNewList = [1;2;3] @ [4;5;6];;

val myNewList : int list = [1; 2; 3; 4; 5; 6]

> myNewList;;
val it : int list = [1; 2; 3; 4; 5; 6]

Let's have a look at some of the most commonly used functions in the List Module: Length, Head, Tail, map, and filter respectively.

The function Length will simply return the length of the list:

> myNewList.Length;;
val it : int = 6

If you want the first element of a list, use Head:

> myNewList.Head;;
val it : int = 1

The rest of the list, meaning all other elements except the Head, is defined as the Tail:

> myNewList.Tail;;
val it : int list = [2; 3; 4; 5; 6]

You can also do some more interesting things with lists, such as calculating the square of all the elements one by one. Note that it's an entirely new list returned from the map function, since lists are immutable. This is done using higher-order functions, where List.map takes a lambda function defined to return the value of x*x as seen in the following code:

> List.map (fun x -> x * x) myNewList;;
val it : int list = [1; 4; 9; 16; 25; 36]

Another interesting function is the filter function of lists, which will return a new list matching the filter criteria:

> List.filter (fun x -> x < 4) myNewList;;
val it : int list = [1; 2; 3]

// Tuple of two floats
(1.0, 2.0)

// Tuple of mixed representations of numbers
(1, 2.0, 3, '4', "four")

// Tuple of expressions
(1.0 + 2.0, 3, 4 + 5)

> (1.0, 2.0);;
val it : float * float = (1.0, 2.0)

> (1, 2.0, 3, '4', "four");;
val it : int * float * int * char * string = (1, 2.0, 3, '4', "four")

> (1.0 + 2.0, 3, 4 + 5);;
val it : float * int * int = (3.0, 3, 9)

let (a, b) = (1.0, 2.0)
printfn "%f %f" a b

let (_, b) = (1.0, 2.0)
printfn "only b %2.2f" b

[0..100]|> List.filter (fun x -> x % 2 = 0)|> List.map (fun x -> x * 2)|> List.sum

val it : int = 5100

Documenting your code is a good practice to get used to. Do you remember details about code you worked on some weeks ago? Then imagine yourself looking at the code you worked on several years ago. This is where documentation comes in. Just some hints about the logic will be sufficient for you and your colleges to grasp the main concepts behind the logic.

(*
This is a comment on multiple lines
*)

/// Single line comment, supporting XML-tags

// This is also a single line comment

The first application for doing something useful will be this Hello World of finance, which will illustrate some powerful yet simple concepts and strengths of F# and functional languages in general.

Let's start our journey into quantitative finance by looking at a simple yet illustrative example using Yahoo finance data. First, we will just put the data into the code to get used to the basic concepts.

First, we put some data in. In F# you can declare a list of strings on multiple lines like the following code:

/// Sample stock data, from Yahoo Finance
let stockData = [
    "2013-06-06,51.15,51.66,50.83,51.52,9848400,51.52";
    "2013-06-05,52.57,52.68,50.91,51.36,14462900,51.36";
    "2013-06-04,53.74,53.75,52.22,52.59,10614700,52.59";
    "2013-06-03,53.86,53.89,52.40,53.41,13127900,53.41";
    "2013-05-31,54.70,54.91,53.99,54.10,12809700,54.10";
    "2013-05-30,55.01,55.69,54.96,55.10,8751200,55.10";
    "2013-05-29,55.15,55.40,54.53,55.05,8693700,55.05"
]

We introduce a function for splitting strings on commas; this will create an array of strings. Don't forget to evaluate the parts of the program in F# Interactive using Alt + Enter. Doing this as a practice will make the number of errors less, and you will also be getting more comfortable and understand the types involved.

The type of the stockData value is not explicitly declared, but if you evaluate it, you should see it is of type string list:

val stockData : string list =
  ["2013-06-06,51.15,51.66,50.83,51.52,9848400,51.52";
   ...
   "2013-05-29,55.15,55.40,54.53,55.05,8693700,55.05"]

// Split row on commas
let splitCommas (l:string) =
    l.Split(',')

// Get the row with lowest trading volume
let lowestVolume =
    stockData
    |> List.map splitCommas
    |> List.minBy (fun x -> (int x.[5]))

Evaluating the expression lowestVolume will parse the strings in stockData and extract the row with the lowest trading volume, column six. Hopefully, the result will be the row with date 2013-05-29, as in the following:

val lowestVolume : string [] =
  [|"2013-05-29"; "55.15"; "55.40"; "54.53"; "55.05"; "8693700";"55.05"|]

The following is the code listing for the program we developed in the previous section, the Hello World program of finance. Try it out for yourself and make changes to it if you like:

/// Open the System.IO namespace
open System.IO

/// Sample stock data, from Yahoo Finance
let stockData = [
    "2013-06-06,51.15,51.66,50.83,51.52,9848400,51.52";
    "2013-06-05,52.57,52.68,50.91,51.36,14462900,51.36";
    "2013-06-04,53.74,53.75,52.22,52.59,10614700,52.59";
    "2013-06-03,53.86,53.89,52.40,53.41,13127900,53.41";
    "2013-05-31,54.70,54.91,53.99,54.10,12809700,54.10";
    "2013-05-30,55.01,55.69,54.96,55.10,8751200,55.10";
    "2013-05-29,55.15,55.40,54.53,55.05,8693700,55.05"
]

/// Split row on commas
let splitCommas (l:string) =
    l.Split(',')


/// Get the row with lowest trading volume
let lowestVolume =
    stockData
    |> List.map splitCommas
    |> List.minBy (fun x -> (int x.[5]))

/// Read a file into a string array
let openFile (name : string) =
    try
        let content = File.ReadAllLines(name)
        content |> Array.toList
    with
        | :? System.IO.FileNotFoundException as e -> printfn "Exception! %s " e.Message; ["empty"]

/// Get the row with lowest trading volume, from file
let lowestVolume =
    openFile filePath
    |> List.map splitCommas
    |> Seq.skip 1
    |> Seq.minBy (fun x -> (int x.[5]))

printfn "Lowest volume, found in row: %A" lowestVolume

> printfn "This works for lists too: %A" [1..5];;
This works for lists too: [1; 2; 3; 4; 5]
val it : unit = ()

/// Open the System.IO namespace
open System.IO

let filePath = @" table.csv"

/// Split row on commas
let splitCommas (l:string) =
    l.Split(',')

/// Read a file into a string array
let openFile (name : string) =
    try
        let content = File.ReadAllLines(name)
        content |> Array.toList
    with
        | :? System.IO.FileNotFoundException as e -> printfn "Exception! %s " e.Message; ["empty"]

/// Get the row with lowest trading volume, from file
let lowestVolume =
    openFile filePath
    |> List.map splitCommas
    |> Seq.skip 1
    |> Seq.minBy (fun x -> (int x.[5]))

/// Use printfn with generic formatter, %A
printfn "Lowest volume, found in row: %A" lowestVolume

Using the interactive mode in Visual Studio and being able to write the program in smaller building blocks using prototyping is a great way of writing software. You have already used this exploratory way of writing programs with the first application.

The workflow is to build up programs incrementally instead of running all code at once. The REPL is a perfect place to try out snippets and experiment with different aspects of F#.

In the preceding example code, we saw that parsing data from a file and extracting various information is straightforward, and results in code that is both easy to read and understand. That's one of the highlights of F#, not less important in quantitative finance where code can be complex and hard to follow and comprehend in many languages.

Let's illustrate the preceding statements with another example. The data in the CSV file in the previous sample application was sorted with the most recent date first. If we want the data to be ordered in a more natural way, lowest date first and so on, we can simply reverse the entire list in the following way:

/// Reverses the price data from the CSV-file
let reversePrices =
    openFile filePath
    |> List.map splitCommas
    |> List.rev

Suppose we are interested in parsing the date column in the example with the stock prices. The entire row looks something like the following:

 [|"2013-02-22"; "54.96"; "55.13"; "54.57"; "55.02"; "5087300"; "55.02"|]

We are interested in the first column, with index 0:

lowestVolume.[0];;	
val it : string = "2013-02-22"

We can make use of the .NET classes for date and time in the System.DateTime namespace:

> let dateTime = System.DateTime.ParseExact(lowestVolume.[0], "yyyy-mm-dd", null);;

val dateTime : System.DateTime = 2013-01-22 00:02:00

Now we have a System.DateTime object, which is compatible with C# and the other .NET languages, to work with!

In this chapter, we had a look into the basics of programming in F# using Visual Studio. We covered a wide variety of the language and scratched the surface of functional programming, where immutability plays a key role. Throughout the chapter we started out illustrating some of F#'s language features and how to make use of the .NET framework. At the end of the chapter, we put together a simple application which shows the power and elegant syntax of F#. Functions are the main building block in any functional programming language. Building new functions from existing ones is a way of abstracting away the complexity and allows for reuse.

In the next chapter, we'll dive into more details about the F# language. You'll learn more about data structures, such as Lists, Sequences, and Arrays. You'll also learn how to structure your program using modules and namespaces, things that will become useful in larger programs. The next chapter will also introduce you to threads, thread pools, asynchronous programming using .NET, and language-specific constructs for the F# language.