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Home > Data > Financial Technology > Learning Quantitative Finance with R
Learning Quantitative Finance with R
Learning Quantitative Finance with R

Learning Quantitative Finance with R: Implement machine learning, time-series analysis, algorithmic trading and more

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Learning Quantitative Finance with R

Chapter 2. Statistical Modeling

In this chapter, we are going to discuss statistical modeling, which will be the first step in learning quantitative finance in R as the concepts of statistical modeling are the driving force for quantitative finance. Before starting this chapter, the assumption is that learners are familiar with basic programming in R and have a sound knowledge of statistical concepts. We will not be discussing statistical concepts in this chapter. We will be discussing how to do the statistical modeling in R.

This chapter covers the following topics:

  • Probability distributions
  • Sampling
  • Statistics
  • Correlation
  • Hypothesis testing
  • Parameter estimation
  • Outlier detection
  • Standardization
  • Normalization

Probability distributions

Probability distributions determine how the values of random variables are spread. For example, the set of all the possible outcomes of the tossing of a sequence of coins gives rise to binomial distribution. The means of large samples of the data population follow normal distribution, which is the most common and useful distribution.

The features of these distributions are very well known and can be used to extract inferences about the population. We are going to discuss in this chapter some of the most common probability distributions and how to compute them.

Normal distribution

Normal distribution is the most widely used probability distribution in the financial industry. It is a bell-shaped curve and mean, median mode is the same for normal distribution. It is denoted by Normal distribution where Normal distribution is the mean and Normal distribution  is the variance of the sample. If the mean is 0 and variance is 1 then the normal distribution is known as standard normal distribution N(1, 0).

Now let...

Sampling

When building any model in finance, we may have very large datasets on which model building will be very time-consuming. Once the model is built, if we need to tweak the model again, it is going to be a time-consuming process because of the volume of data. So it is better to get the random or proportionate sample of the population data on which model building will be easier and less time-consuming. So in this section, we are going to discuss how to select a random sample and a stratified sample from the data. This will play a critical role in building the model on sample data drawn from the population data.

Random sampling

Select the sample where all the observation in the population has an equal chance. It can be done in two ways, one without replacement and the other with replacement.

A random sample without replacement can be done by executing the following code:

> RandomSample <- Sampledata[sample(1:nrow(Sampledata), 10,  
>+ replace=FALSE),]

This generates the following...

Statistics

In a given dataset, we try to summarize the data by the central position of the data, which is known as measure of central tendency or summary statistics. There are several ways to measure the central tendency, such as mean, median, and mode. Mean is the widely used measure of central tendency. Under different scenarios, we use different measures of central tendency. Now we are going to give an example of how to compute the different measures of central tendency in R.

Mean

mean is the equal weightage average of the sample. For example, we can compute the mean of Volume in the dataset Sampledata by executing the following code, which gives the arithmetic mean of the volume:

mean(Sampledata$Volume)

Median

Median is the mid value of the matrix when it is arranged in a sorted way, which can be computed by executing the following code:

median(Sampledata$Volume)

Mode

Mode is the value present in the attribute which has maximum frequency. For mode, there does not exist an inbuilt function...

Correlation

Correlation plays a very important role in quant finance. It not only determines the relation between the financial attributes but also plays a crucial role in predicting the future of financial instruments. Correlation is the measure of linear relationship between the two financial attributes. Now let us try to compute the different types of correlation in R using Sampledata, which is used in identifying the orders of components of predictive financial models.

Correlation can be computed by the following code. Let's first subset the data and then run the function for getting correlation:

x<-Sampledata[,2:5] 
rcorr(x, type="pearson")

This generates the following correlation matrix, which shows the measure of linear relationship between the various daily level prices of a stock:

Open

High

Low

Close

Open

1

0.962062

0.934174

0.878553

High

0.962062

1

0.952676

0.945434

Low

0.934174

0.952676

1

0.960428

Close

0.878553

0.945434

...

Probability distributions

Probability distributions determine how the values of random variables are spread. For example, the set of all the possible outcomes of the tossing of a sequence of coins gives rise to binomial distribution. The means of large samples of the data population follow normal distribution, which is the most common and useful distribution.

The features of these distributions are very well known and can be used to extract inferences about the population. We are going to discuss in this chapter some of the most common probability distributions and how to compute them.

Normal distribution

Normal distribution is the most widely used probability distribution in the financial industry. It is a bell-shaped curve and mean, median mode is the same for normal distribution. It is denoted by  where  is the mean and  is the variance of the sample. If the mean is 0 and variance is 1 then the normal distribution is known as standard normal distribution N(1, 0).

Now let us discuss the main...

Sampling

When building any model in finance, we may have very large datasets on which model building will be very time-consuming. Once the model is built, if we need to tweak the model again, it is going to be a time-consuming process because of the volume of data. So it is better to get the random or proportionate sample of the population data on which model building will be easier and less time-consuming. So in this section, we are going to discuss how to select a random sample and a stratified sample from the data. This will play a critical role in building the model on sample data drawn from the population data.

Random sampling

Select the sample where all the observation in the population has an equal chance. It can be done in two ways, one without replacement and the other with replacement.

A random sample without replacement can be done by executing the following code:

> RandomSample <- Sampledata[sample(1:nrow(Sampledata), 10,  
>+ replace=FALSE),]

This generates the...

Statistics

In a given dataset, we try to summarize the data by the central position of the data, which is known as measure of central tendency or summary statistics. There are several ways to measure the central tendency, such as mean, median, and mode. Mean is the widely used measure of central tendency. Under different scenarios, we use different measures of central tendency. Now we are going to give an example of how to compute the different measures of central tendency in R.

Mean

mean is the equal weightage average of the sample. For example, we can compute the mean of Volume in the dataset Sampledata by executing the following code, which gives the arithmetic mean of the volume:

mean(Sampledata$Volume)

Median

Median is the mid value of the matrix when it is arranged in a sorted way, which can be computed by executing the following code:

median(Sampledata$Volume)

Mode

Mode is the value present in the attribute which has maximum frequency. For mode, there does not exist an inbuilt...

Correlation

Correlation plays a very important role in quant finance. It not only determines the relation between the financial attributes but also plays a crucial role in predicting the future of financial instruments. Correlation is the measure of linear relationship between the two financial attributes. Now let us try to compute the different types of correlation in R using Sampledata, which is used in identifying the orders of components of predictive financial models.

Correlation can be computed by the following code. Let's first subset the data and then run the function for getting correlation:

x<-Sampledata[,2:5] 
rcorr(x, type="pearson")

This generates the following correlation matrix, which shows the measure of linear relationship between the various daily level prices of a stock:

Open

High

Low

Close

Open

1

0.962062

0.934174

0.878553

High

0.962062

1

0.952676

0.945434

Low

0.934174

0.952676

1

0.960428

Close

0.878553

0.945434

0.960428...

Hypothesis testing

Hypothesis testing is used to reject or retain a hypothesis based upon the measurement of an observed sample. We will not be going into theoretical aspects but will be discussing how to implement the various scenarios of hypothesis testing in R.

Lower tail test of population mean with known variance

The null hypothesis is given by  where is the hypothesized lower bound of the population mean.

Let us assume a scenario where an investor assumes that the mean of daily returns of a stock since inception is greater than $10. The average of 30 days' daily return sample is $9.9. Assume the population standard deviation is 0.011. Can we reject the null hypothesis at .05 significance level?

Now let us calculate the test statistics z which can be computed by the following code in R:

> xbar= 9.9           
> mu0 = 10            
> sig = 1.1            
> n = 30                  
> z = (xbar-mu0)/(sig/sqrt(n))  
> z

Here:

  • xbar: Sample...

Parameter estimates

In this section, we are going to discuss some of the algorithms used for parameter estimation.

Maximum likelihood estimation

Maximum likelihood estimation (MLE) is a method for estimating model parameters on a given dataset.

Now let us try to find the parameter estimates of a probability density function of normal distribution.

Let us first generate a series of random variables, which can be done by executing the following code:

> set.seed(100) 
> NO_values <- 100 
> Y <- rnorm(NO_values, mean = 5, sd = 1) 
> mean(Y)

This gives 5.002913.

> sd(Y)

This gives 1.02071.

Now let us make a function for log likelihood:

LogL <- function(mu, sigma) { 
+      A = dnorm(Y, mu, sigma) 
+      -sum(log(A)) 
+  }

Now let us apply the function mle to estimate the parameters for estimating mean and standard deviation:

  > library(stats4) 
> mle(LogL, start = list(mu = 2, sigma=2))

mu and sigma have been...

Outlier detection

Outliers are very important to be taken into consideration for any analysis as they can make analysis biased. There are various ways to detect outliers in R and the most common one will be discussed in this section.

Boxplot

Let us construct a boxplot for the variable volume of the Sampledata, which can be done by executing the following code:

> boxplot(Sampledata$Volume, main="Volume", boxwex=0.1)

The graph is as follows:

Figure 2.16: Boxplot for outlier detection

An outlier is an observation which is distant from the rest of the data. When reviewing the preceding boxplot, we can clearly see the outliers which are located outside the fences (whiskers) of the boxplot.

LOF algorithm

The local outlier factor (LOF) is used for identifying density-based local outliers. In LOF, the local density of a point is compared with that of its neighbors. If the point is in a sparser region than its neighbors then it is treated as an outlier. Let us consider some of the variables from...

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Key benefits

  • Understand the basics of R and how they can be applied in various Quantitative Finance scenarios
  • Learn various algorithmic trading techniques and ways to optimize them using the tools available in R.
  • Contain different methods to manage risk and explore trading using Machine Learning.

Description

The role of a quantitative analyst is very challenging, yet lucrative, so there is a lot of competition for the role in top-tier organizations and investment banks. This book is your go-to resource if you want to equip yourself with the skills required to tackle any real-world problem in quantitative finance using the popular R programming language. You'll start by getting an understanding of the basics of R and its relevance in the field of quantitative finance. Once you've built this foundation, we'll dive into the practicalities of building financial models in R. This will help you have a fair understanding of the topics as well as their implementation, as the authors have presented some use cases along with examples that are easy to understand and correlate. We'll also look at risk management and optimization techniques for algorithmic trading. Finally, the book will explain some advanced concepts, such as trading using machine learning, optimizations, exotic options, and hedging. By the end of this book, you will have a firm grasp of the techniques required to implement basic quantitative finance models in R.

Who is this book for?

If you want to learn how to use R to build quantitative finance models with ease, this book is for you. Analysts who want to learn R to solve their quantitative finance problems will also find this book useful. Some understanding of the basic financial concepts will be useful, though prior knowledge of R is not required.

What you will learn

  • Get to know the basics of R and how to use it in the field of Quantitative Finance
  • Understand data processing and model building using R
  • Explore different types of analytical techniques such as statistical analysis, time-series analysis, predictive modeling, and econometric analysis
  • Build and analyze quantitative finance models using real-world examples
  • How real-life examples should be used to develop strategies
  • Performance metrics to look into before deciding upon any model
  • Deep dive into the vast world of machine-learning based trading
  • Get to grips with algorithmic trading and different ways of optimizing it
  • Learn about controlling risk parameters of financial instruments
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Publication date : Mar 23, 2017
Length: 284 pages
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Language : English
ISBN-13 : 9781786462411
Category :
Data
Languages :
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Concepts :
Financial Technology

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Publication date : Mar 23, 2017
Length: 284 pages
Edition : 1st
Language : English
ISBN-13 : 9781786462411
Category :
Data
Languages :
R
Concepts :
Financial Technology

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Table of Contents

9 Chapters
1. Introduction to R Chevron down icon Chevron up icon
1. Introduction to R
The need for R
How to download/install R
How to install packages
Data types
Importing and exporting different data types
How to write code expressions
Functions
Loops (for, while, if, and if...else)
Loop control statements
Questions
Summary
2. Statistical Modeling Chevron down icon Chevron up icon
2. Statistical Modeling
Probability distributions
Sampling
Statistics
Correlation
Hypothesis testing
Parameter estimates
Outlier detection
Standardization
Normalization
Questions
Summary
3. Econometric and Wavelet Analysis Chevron down icon Chevron up icon
3. Econometric and Wavelet Analysis
Simple linear regression
Multivariate linear regression
Multicollinearity
ANOVA
Feature selection
Stepwise variable selection
Ranking of variables
Wavelet analysis
Fast Fourier transformation
Hilbert transformation
Questions
Summary
4. Time Series Modeling Chevron down icon Chevron up icon
4. Time Series Modeling
General time series
Converting data to time series
zoo
xts
Linear filters
AR
MA
ARIMA
GARCH
EGARCH
VGARCH
Dynamic conditional correlation
Questions
Summary
5. Algorithmic Trading Chevron down icon Chevron up icon
5. Algorithmic Trading
Momentum or directional trading
Capital asset pricing model
Multi factor model
Portfolio construction
Questions
Summary
6. Trading Using Machine Learning Chevron down icon Chevron up icon
6. Trading Using Machine Learning
Logistic regression neural network
Neural network
Deep neural network
K means algorithm
K nearest neighborhood
Support vector machine
Decision tree
Random forest
Questions
Summary
7. Risk Management Chevron down icon Chevron up icon
7. Risk Management
Market risk
Portfolio risk
VaR
Monte Carlo simulation
Hedging
Basel regulation
Credit risk
Fraud detection
Liability management
Questions
Summary
8. Optimization Chevron down icon Chevron up icon
8. Optimization
Dynamic rebalancing
Walk forward testing
Grid testing
Genetic algorithm
Questions
Summary
9. Derivative Pricing Chevron down icon Chevron up icon
9. Derivative Pricing
Option pricing
Implied volatility
Bond pricing
Credit spread
Credit default swaps
Interest rate derivatives
Exotic options
Questions
Summary

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Customer reviews

Rating distribution
Full star icon Full star icon Full star icon Half star icon Empty star icon 3.7
(3 Ratings)
5 star 66.7%
4 star 0%
3 star 0%
2 star 0%
1 star 33.3%
Manuel Amunategui Mar 31, 2017
Full star icon Full star icon Full star icon Full star icon Full star icon 5
I’d like to recommend this book to those looking for wide coverage on quantitative finance using the R language (but I am biased as I was the technical reviewer for the book :-) For those who know me and my blog (amunategui.github.io), know that I always appreciate easy to understand language and lots of hands-on examples, and this book is built on such foundation.This book offers a great overview of many R libraries covering topics from financial probability and modeling all the way to trading, derivatives, and risk management - and my personal favorites - algorithmic trading and derivative pricing.
Amazon Verified review Amazon
Amazon Customer Aug 21, 2018
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Very nicely written book and easy to understand. I received the book today and gone through the first chapter it is really easy to understand as an amateur in the field of R. Thanks to the authors who wrote the book from the beginner's perspective. One thing that must be added with the book is the CD for the exercises.
Amazon Verified review Amazon
Lindarden07 Sep 23, 2017
Full star icon Empty star icon Empty star icon Empty star icon Empty star icon 1
This book gives a list of functions for each topic. No detailed explanation is given. It serves as a reference to see which package and function you need to use to address some problems you are facing. But for detailed content, look for somewhere else.
Amazon Verified review Amazon

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About the authors

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Profile icon Jeet
Jeet
Dr. Param Jeet is a Ph.D. in mathematics from one of India's leading technological institute in Madras (IITM), India. Dr. Param Jeet has a couple of mathematical research papers published in various international journals. Dr. Param Jeet has been into the analytics industry for the last few years and has worked with various leading multinational companies as well as consulted few of companies as a data scientist.
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Profile icon PRASHANT VATS
PRASHANT VATS
Prashant Vats is a masters in mathematics from one of India's leading technological institute, IIT Mumbai. Prashant has been into analytics industry for more than 10 years and has worked with various leading multinational companies as well as consulted few of companies as data scientist across several domain.
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USA:

'

Economy: Delivery to most addresses in the US within 10-15 business days

Premium: Trackable Delivery to most addresses in the US within 3-8 business days

UK:

Economy: Delivery to most addresses in the U.K. within 7-9 business days.
Shipments are not trackable

Premium: Trackable delivery to most addresses in the U.K. within 3-4 business days!
Add one extra business day for deliveries to Northern Ireland and Scottish Highlands and islands

EU:

Premium: Trackable delivery to most EU destinations within 4-9 business days.

Australia:

Economy: Can deliver to P. O. Boxes and private residences.
Trackable service with delivery to addresses in Australia only.
Delivery time ranges from 7-9 business days for VIC and 8-10 business days for Interstate metro
Delivery time is up to 15 business days for remote areas of WA, NT & QLD.

Premium: Delivery to addresses in Australia only
Trackable delivery to most P. O. Boxes and private residences in Australia within 4-5 days based on the distance to a destination following dispatch.

India:

Premium: Delivery to most Indian addresses within 5-6 business days

Rest of the World:

Premium: Countries in the American continent: Trackable delivery to most countries within 4-7 business days

Asia:

Premium: Delivery to most Asian addresses within 5-9 business days

Disclaimer:
All orders received before 5 PM U.K time would start printing from the next business day. So the estimated delivery times start from the next day as well. Orders received after 5 PM U.K time (in our internal systems) on a business day or anytime on the weekend will begin printing the second to next business day. For example, an order placed at 11 AM today will begin printing tomorrow, whereas an order placed at 9 PM tonight will begin printing the day after tomorrow.


Unfortunately, due to several restrictions, we are unable to ship to the following countries:

  1. Afghanistan
  2. American Samoa
  3. Belarus
  4. Brunei Darussalam
  5. Central African Republic
  6. The Democratic Republic of Congo
  7. Eritrea
  8. Guinea-bissau
  9. Iran
  10. Lebanon
  11. Libiya Arab Jamahriya
  12. Somalia
  13. Sudan
  14. Russian Federation
  15. Syrian Arab Republic
  16. Ukraine
  17. Venezuela
What is custom duty/charge? Chevron down icon Chevron up icon

Customs duty are charges levied on goods when they cross international borders. It is a tax that is imposed on imported goods. These duties are charged by special authorities and bodies created by local governments and are meant to protect local industries, economies, and businesses.

Do I have to pay customs charges for the print book order? Chevron down icon Chevron up icon

The orders shipped to the countries that are listed under EU27 will not bear custom charges. They are paid by Packt as part of the order.

List of EU27 countries: www.gov.uk/eu-eea:

A custom duty or localized taxes may be applicable on the shipment and would be charged by the recipient country outside of the EU27 which should be paid by the customer and these duties are not included in the shipping charges been charged on the order.

How do I know my custom duty charges? Chevron down icon Chevron up icon

The amount of duty payable varies greatly depending on the imported goods, the country of origin and several other factors like the total invoice amount or dimensions like weight, and other such criteria applicable in your country.

For example:

  • If you live in Mexico, and the declared value of your ordered items is over $ 50, for you to receive a package, you will have to pay additional import tax of 19% which will be $ 9.50 to the courier service.
  • Whereas if you live in Turkey, and the declared value of your ordered items is over € 22, for you to receive a package, you will have to pay additional import tax of 18% which will be € 3.96 to the courier service.
How can I cancel my order? Chevron down icon Chevron up icon

Cancellation Policy for Published Printed Books:

You can cancel any order within 1 hour of placing the order. Simply contact customercare@packt.com with your order details or payment transaction id. If your order has already started the shipment process, we will do our best to stop it. However, if it is already on the way to you then when you receive it, you can contact us at customercare@packt.com using the returns and refund process.

Please understand that Packt Publishing cannot provide refunds or cancel any order except for the cases described in our Return Policy (i.e. Packt Publishing agrees to replace your printed book because it arrives damaged or material defect in book), Packt Publishing will not accept returns.

What is your returns and refunds policy? Chevron down icon Chevron up icon

Return Policy:

We want you to be happy with your purchase from Packtpub.com. We will not hassle you with returning print books to us. If the print book you receive from us is incorrect, damaged, doesn't work or is unacceptably late, please contact Customer Relations Team on customercare@packt.com with the order number and issue details as explained below:

  1. If you ordered (eBook, Video or Print Book) incorrectly or accidentally, please contact Customer Relations Team on customercare@packt.com within one hour of placing the order and we will replace/refund you the item cost.
  2. Sadly, if your eBook or Video file is faulty or a fault occurs during the eBook or Video being made available to you, i.e. during download then you should contact Customer Relations Team within 14 days of purchase on customercare@packt.com who will be able to resolve this issue for you.
  3. You will have a choice of replacement or refund of the problem items.(damaged, defective or incorrect)
  4. Once Customer Care Team confirms that you will be refunded, you should receive the refund within 10 to 12 working days.
  5. If you are only requesting a refund of one book from a multiple order, then we will refund you the appropriate single item.
  6. Where the items were shipped under a free shipping offer, there will be no shipping costs to refund.

On the off chance your printed book arrives damaged, with book material defect, contact our Customer Relation Team on customercare@packt.com within 14 days of receipt of the book with appropriate evidence of damage and we will work with you to secure a replacement copy, if necessary. Please note that each printed book you order from us is individually made by Packt's professional book-printing partner which is on a print-on-demand basis.

What tax is charged? Chevron down icon Chevron up icon

Currently, no tax is charged on the purchase of any print book (subject to change based on the laws and regulations). A localized VAT fee is charged only to our European and UK customers on eBooks, Video and subscriptions that they buy. GST is charged to Indian customers for eBooks and video purchases.

What payment methods can I use? Chevron down icon Chevron up icon

You can pay with the following card types:

  1. Visa Debit
  2. Visa Credit
  3. MasterCard
  4. PayPal
What is the delivery time and cost of print books? Chevron down icon Chevron up icon

Shipping Details

USA:

'

Economy: Delivery to most addresses in the US within 10-15 business days

Premium: Trackable Delivery to most addresses in the US within 3-8 business days

UK:

Economy: Delivery to most addresses in the U.K. within 7-9 business days.
Shipments are not trackable

Premium: Trackable delivery to most addresses in the U.K. within 3-4 business days!
Add one extra business day for deliveries to Northern Ireland and Scottish Highlands and islands

EU:

Premium: Trackable delivery to most EU destinations within 4-9 business days.

Australia:

Economy: Can deliver to P. O. Boxes and private residences.
Trackable service with delivery to addresses in Australia only.
Delivery time ranges from 7-9 business days for VIC and 8-10 business days for Interstate metro
Delivery time is up to 15 business days for remote areas of WA, NT & QLD.

Premium: Delivery to addresses in Australia only
Trackable delivery to most P. O. Boxes and private residences in Australia within 4-5 days based on the distance to a destination following dispatch.

India:

Premium: Delivery to most Indian addresses within 5-6 business days

Rest of the World:

Premium: Countries in the American continent: Trackable delivery to most countries within 4-7 business days

Asia:

Premium: Delivery to most Asian addresses within 5-9 business days

Disclaimer:
All orders received before 5 PM U.K time would start printing from the next business day. So the estimated delivery times start from the next day as well. Orders received after 5 PM U.K time (in our internal systems) on a business day or anytime on the weekend will begin printing the second to next business day. For example, an order placed at 11 AM today will begin printing tomorrow, whereas an order placed at 9 PM tonight will begin printing the day after tomorrow.


Unfortunately, due to several restrictions, we are unable to ship to the following countries:

  1. Afghanistan
  2. American Samoa
  3. Belarus
  4. Brunei Darussalam
  5. Central African Republic
  6. The Democratic Republic of Congo
  7. Eritrea
  8. Guinea-bissau
  9. Iran
  10. Lebanon
  11. Libiya Arab Jamahriya
  12. Somalia
  13. Sudan
  14. Russian Federation
  15. Syrian Arab Republic
  16. Ukraine
  17. Venezuela