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
Itos lemma
The Black-Scholes formula
Implied volatility
SECTION III: NUMERICAL METHODS IN FINANCE
Monte Carlo Simulation
The basic concept of Monte Carlo simulation
Variance reduction method
Exotic option
Multi asset options
Control variates method
Derivative Pricing with Partial Differential Equation
Explicit method
Implicit method
Noise reduction via Kalman Filter
Introduction to Kalman filter
Nonlinear Kalman filter
SECTION IV: APPENDIX 237
A Optimization with R
A.1 Multi variate optimization problem
A.2 Efficient frontier by optimization problem
B Noise reduction via Kalman Filter
B.1 Introduction to Kalman filter
B.2 Nonlinear Kalman filter
C The other references on R
C.1 Information sources on R
C.2 R package on finance
References
Index
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