R Programming and Its Applications in Financial Mathematics

Shuichi Ohsaki, Jori Ruppert-Felsot, Daisuke Yoshikawa

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9781351649865
• Topic: Business
• Subtopic: Finance
• Index: Business

This book provides an introduction to R programming and a summary of financial mathematics.

It is not always easy for graduate students to grasp an overview of the theory of finance in an abstract form. For newcomers to the finance industry, it is not always obvious how to apply the abstract theory to the real financial data they encounter. Introducing finance theory alongside numerical applications makes it easier to grasp the subject.

Popular programming languages like C++, which are used in many financial applications are meant for general-purpose requirements. They are good for implementing large-scale distributed systems for simultaneously valuing many financial contracts, but they are not as suitable for small-scale ad-hoc analysis or exploration of financial data. The R programming language overcomes this problem. R can be used for numerical applications including statistical analysis, time series analysis, numerical methods for pricing financial contracts, etc.

This book provides an overview of financial mathematics with numerous examples numerically illustrated using the R programming language.

CONTENTS

Preface

1 Introduction to R Programming

1.1 Installation of R

1.2 Operators

1.3 Data structure

1.3.1 Scalar

1.3.2 Vector

1.3.3 Matrix

1.3.4 List

1.3.5 Data frame

1.3.6 Factor

1.3.7 Investigation of types and structures of data

1.4 Functions

1.5 Control statements

1.5.1 if-statement

1.5.2 Iterative processing: for-statement, while-statement

1.6 Graphics

1.7 Reading and writing data

1.8 Reading program

1.9 Packages

SECTION I STATISTICS IN FINANCE

2 Statistical Analysis with R

2.1 Basic statistics

2.2 Probability distribution and random numbers

2.3 Hypothesis testing

2.3.1 What is hypothesis testing?

2.3.2 t-Test of population mean

2.4 Regression Analysis

2.5 Yield curve analysis using principal component analysis

2.5.1 Yield curve

2.5.2 What is principal component analysis?

2.5.3 Example of principal component analysis using JGB

2.5.4 How to calculate the principal component analysis?

3 Time Series Analysis with R

3.1 Preparation of time series data

3.2 Before applying for models

3.3 The application of the AR model

3.3.1 Residual analysis

3.3.2 Forecasting

3.4 Models extended from AR

3.4.1 ARMA and ARIMA model

3.4.2 Vector autoregressive

3.4.3 GARCH model

3.4.4 Cointegration

3.5 Application of the time series analysis to finance: Pairs trading

SECTION II BASIC THEORY OF FINANCE

4 Modern Portfolio Theory and CAPM

4.1 Mean‐variance portfolio

4.2 Market portfolio

4.3 Derivation of CAPM

4.4 The extension of CAPM: Multi‐factor model

4.4.1 Arbitrage Pricing Theory

4.4.2 Fama‐French’s 3 factor model

4.5 The form of the efficient frontier

5 Interest Rate Swap and Discount Factor

5.1 Interest rate swap

5.2 Pricing of interest rate swaps and the derivation of discount factors

5.3 Valuation of interest rate swaps and their risk

6 Discrete Time Model: Tree Model

6.1 Single period binomial model

6.1.1 Derivative pricing

6.1.2 Pricing by risk neutral measure

6.2 Multi period binomial model

6.2.1 Generalization to the multi period model

6.2.2 Pricing call options

6.3 Trinomial model

7 Continuous Time Model and the Black‐Scholes Formula

7.1 Continuous rate of return

7.2 Itô s lemma

7.3 The Black‐Scholes formula

7.4 Implied volatility

SECTION III NUMERICAL METHODS IN FINANCE

8 Monte Carlo Simulation

8.1 The basic concept of Monte Carlo simulation

8.2 Variance reduction method

8.2.1 Antithetic variates method

8.2.2 Moment matching method

8.3 Exotic options

8.4 Multi asset options

8.5 Control variates method

9 Derivative Pricing with Partial Diff...

Table of contents

• Cover
• Halftitle Page
• Title Page
• Copyright
• Table of Contents