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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 Meanāvariance portfolio
4.2 Market portfolio
4.3 Derivation of CAPM
4.4 The extension of CAPM: Multiāfactor model
4.4.1 Arbitrage Pricing Theory
4.4.2 FamaāFrenchās 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 BlackāScholes Formula
7.1 Continuous rate of return
7.2 ItƓ s lemma
7.3 The BlackāScholes 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...
