R Programming and Its Applications in Financial Mathematics

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. Preface Introduction to R programming Installation of R Operators Data structure Functions Control statements Graphics Reading and writing data Reading program Packages SECTION I: STATISTICS IN FINANCE Statistical Analysis with R Basic Statistics Probability distribution and random numbers Hypothesis testing Regression Analysis Yield curve analysis using principal component analysis? Time Series Analysis with R Preparation of time series data Before applying for models The application for AR model Models extended from AR Application of the time series analysis to finance: Pair trading Nonlinear statistics with R ARCH and GARCH Nonparametric Functional Data Analysis SECTION II: BASIC THEORY OF FINANCE Modern Portfolio Theory and CAPM Mean-variance portfolio Market portfolio Derivation of CAPM The extension of CAPM: Multi-factor model The form of efficient frontier Interest Rate Swap and Discount Factor Interest rate swap Pricing of interest rate swap and derivation of discount factors Valuation of interest rate swap and risk analysis Discrete Time Model: Tree Model Single period binomial model Multi period binomial model Trinomial model Continuous time model and the Black-Scholes Formula Continuous rate of return Itˆo’s lemma The Black-Scholes formula Implied volatility SECTION III: NUMERICAL METHODS IN FINANCE Monte Carlo Simulation The basic concept of Mon