Quantitative Finance with SAS

What is Quantitative Finance

Quantitative Finance is also known as Mathematical Finance and it is a field of applied mathematics which is related with financial markets. Mathematical finance also overlaps with computational finance and financial engineering. There are a lot of advanced quantitative techniques which are used in different fields in today’s world.

Course Objectives

At the end of this course you will be able to

• Install SAS and use it for real time financial analysis
• Implement financial analysis concepts using SAS inbuilt quantitative procedures
• Learn about the T test and its practical examples
• Know more about correlation theory and regression modelling in SAS

Course Description

Section 1: Overview of SAS and Quantitative Finance

Introduction to SAS Quantitative Finance

SAS is the most comprehensive statistical analysis software used widely in the world. SAS offers data analysis solutions to almost all fields through various statistical models. Each analysis in SAS is performed through a subroutine called procedure (PROC). PROC QTL is a user defined SAS procedure which is used to map quantitative trait loci. SAS can be used for learning statistics and quantitative methods. This chapter gives a quick introduction to SAS and Quantitative finance in SAS.

Installation of SAS.

This chapter explains how to install SAS software for different OS. The system requirements of SAS are also included in this chapter

SAS System & Means Procedure

The MEANS procedure is a data summarization tool which is used to calculate descriptive statistics for all observations and within group of observations. PROC MEANS and PROC SUMMARY are more similar to each other. PROC MEANS gives a output and there are two types of such output – PROC MEANS default output and PROC MEANS Customized Output. PROC MEANS is also used to perform a t test. In this chapter the PROC MEANS, its output, syntax, task and statistical computations are explained in detail.

Section 2: Concept of T Test

T Test

The TTEST procedure in SAS is used to perform t tests for one sample, two sample and paired observations. The assumptions of all these three t tests are given in this chapter. The topics covered in this section are

• One sample t test – compares a sample mean to a given value. Example is given for your reference
• Comparing group means – Group t test is used to compare values from two different groups where the data are normally distributed in each group. Examples of group t test are provided
• Syntax of PROC TTEST
• PROC TTEST Statements – BY statement, CLASS statement, FREQ statement, PAIRED Statement, VAR Statement, WEIGHT Statement
• Computational methods – The t Statistic, The Folded Form F Statistic, The Approximate t Statistic, Satterthwaite’s Approximation, The Cochran and Cox Approximation, Confidence Interval Estimation
• Displayed Output
• ODS Table Names

Practical of T Test

Three examples are given in this section to make you understand about t tests easily

• Example 1 – Comparing Group Means Using Input Data Set of Summary Statistics
• Example 2 – One-Sample Comparison Using the FREQ Statement
• Example 3 – Paired Comparisons

Section 3: Correlation Theory

Introduction to Correlation theory

Correlation is a method where one variable increases and the other variable decreases. For example, if there is a rise in temperature it will also lead to a rise in the sales of ice creams. This is called positive correlation. Correlation analysis deals with relationship among variables. The correlation coefficient lets researchers to measure if there is a possible linear relationship between two variables measured on the same subject. The values of the correlation coefficient are always between -1 and +1. There are different types of correlation coefficients used for different situation. The most common is the Pearson correlation coefficient. This chapter contains more details about the correlation theory and explains its types in detail.

Interpretation of SAS Output

The output produced by PROC CORR in SAS gives a lot of useful information. The output contains information regarding the list of variables included in the analysis. Next it provides a list of simple statistics for each variable in the analysis. This list contains the number of observations, mean, standard deviation, sum, minimum and maximum. One list contains each variable and their label. Finally the correlation measures are provided in the output. The output will be named “Pearson Correlation Coefficient” by default. The results will be displayed in a cross tabular format with the values of one on the diagonal. This section explains the output and correlation procedure using an example.

Correlation theory and implementation in SAS

The PROC CORR procedure is used to measure correlation in SAS. This procedure will provide correlation measures of multiple variables which is in a cross tabular format. The syntax used for correlation in SAS is mentioned in detail along with its parameters which are mentioned below

• Dataset – name of the data set which needs to be analyzed
• By – produces separate correlation analysis for each BY group
• Freq – identifies a variable whose values represent the frequency of each observation
• partial – identifies controlling variables to compute different types of correlation coefficient
• var – identifies controlling variables to correlate and their order in the matrix
• weight – identifies a variable whose values weight each observation in order to compute Pearson weight product moment correlation
• with – computes correlation for specific combination of variables

This chapter will let you learn how to use the CORR procedure to tell SAS to calculate Pearson Correlation Coefficient. You will also learn how to tell SAS to perform other alternative coefficients. You will learn to read typical correlation procedure output in SAS and interpret a correlation coefficient.

Section 4: Regression Modelling

Introduction to Regression Modelling

Regression analysis is the analysis of relationship between a response and the another set of variable. The regression analysis finds out a response variable and parameters. In order to perform regression analysis in SAS the PROC REG procedure is used. This procedure will provide regression analysis for multiple variables. The syntax for the procedure is explained in detail which contains

• dataset
• by var
• depvar
• indep var
• freq var
• weight var

There are different types of regression which are also explained in this chapter in detail with examples

• Simple Linear Regression
• Polynomial Regression
• Response Surface Regression
• Partial Least Squares regression
• Quantile Regression
• Robust Regression
• Regression with Transformation

In this chapter you will learn how to use the REG procedure in SAS to calculate regression equation between two numeric variables. You will also learn how to use MODEL and PLOT statement to inform SAS how each variable should be treated. Here you will learn how to use the REG procedure to conduct regression analysis in SAS which involves quadratic terms and transformed variables.

Regression Modelling in SAS System

This lesson will help you to find how SAS can be used to test whether the data meets the assumptions of Linear regression. In this chapter the following assumptions are considered

• Linearity – In this assumption the relationships between the predicators and the outcome are considered to be linear
• Normality – The assumption here is that the errors are normally distributed
• Homogeneity of Variance – The error variance are constant
• Independence – The assumption here is the errors of one observation are not correlated with errors of any other observation.
• Errors in Variables – Here the assumption is the predicator variables are determined without error
• Model Specification – The models are properly specified

Analysis of Variance

ANOVA is SAS is done using PROC ANOVA. It is used to perform ANOVA for balanced data from a wide variety of experimental designs. ANOVA is used to compare the means of multiple groups. The ANOVA procedure is one of the several procedures in SAS. The basic syntax for ANOVA in SAS is given in this chapter with the explanations for each of the parameters used in the syntax. The topics included in this section are

• One way layout with Means Comparison
• Randomized Complete Block with One Factor
• ANOVA Procedure – ABSORB statement, BY Statement, CLASS, FREQ, MANOVA, MEANS, MODEL, REPEATED and TEST statements
• Missing values
• Computational Method
• Output
• ODS Table names and graphics
• Examples of ANOVA using SAS

Parameter Estimates

Parameter estimates are a part of PROC REG in SAS. The parameter estimates table and the associated statistics in PROC REG are explained in detail in this chapter using an example.

Example of Maruti vs Sensex

This section contains the example of Maruti Vs Sensex calculation using SAS.

Section 5: Multiple Regression Modelling

Introduction theory to SAS procedures

SAS procedures are used to carry out all form of statistical analysis in SAS. The keyword for procedure in SAS starts with PROC. The most commonly used SAS procedure steps are explained in detail in this chapter.

SAS procedures – Economic Data

The SAS access to financial and economic databases are provided in this chapter and it explains about the DATASOURCE procedure and its features.

Interpretations of SAS Output

This section deals with various types of interpretation of SAS output.

Interpretation of BSE – Sensex

This chapter will help you to understand how SAS is used in the calculation of Sensex.

Interpretation of Forex

Under this chapter you will learn how to interpret Forex.