R Programming and Its Applications in Financial Mathematics (Hardcover)

Preface

Introduction to R programming

Installation of R

Operators

Data structure

Functions

Control statements

Graphics

Reading and writing data

Reading program

Packages

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

ARCH and GARCH

Nonparametric

Functional Data Analysis

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

It?o’s lemma

The Black-Scholes formula

Implied volatility

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

A.1 Multi variate optimization problem

A.2 Efficient frontier by optimization problem

B.1 Introduction to Kalman filter

B.2 Nonlinear Kalman filter

C.1 Information sources on R

C.2 R package on finance