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E-raamat: R Programming and Its Applications in Financial Mathematics

(Hokkai-Gakuen University, Sapporo, Japan), , (Bank of America Merrill Lynch, Shinjuku-ku, Japan)
  • Formaat: 258 pages
  • Ilmumisaeg: 31-Jan-2018
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9781498766104
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R Programming and Its Applications in Financial MathematicsSuurem pilt
  • Formaat: 258 pages
  • Ilmumisaeg: 31-Jan-2018
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9781498766104
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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 v
1 Introduction to R Programming
1(40)
1.1 Installation of R
2(4)
1.2 Operators
6(1)
1.3 Data structure
7(15)
1.3.1 Scalar
9(2)
1.3.2 Vector
11(3)
1.3.3 Matrix
14(3)
1.3.4 List
17(3)
1.3.5 Data frame
20(1)
1.3.6 Factor
21(1)
1.3.7 Investigation of types and structures of data
22(1)
1.4 Functions
22(2)
1.5 Control statements
24(5)
1.5.1 If Statement
25(2)
1.5.2 Iterative processing: for statement, while statement
27(2)
1.6 Graphics
29(4)
1.7 Reading and writing data
33(1)
1.8 Reading program
34(2)
1.9 Packages
36(5)
SECTION I STATISTICS IN FINANCE
2 Statistical Analysis with R
41(32)
2.1 Basic statistics
41(5)
2.2 Probability distribution and random numbers
46(1)
2.3 Hypothesis testing
47(7)
2.3.1 What is hypothesis testing?
47(2)
2.3.2 t-Test of population mean
49(5)
2.4 Regression Analysis
54(5)
2.5 Yield curve analysis using principal component analysis
59(14)
2.5.1 Yield curve
59(2)
2.5.2 What is principal component analysis?
61(3)
2.5.3 Example of principal component analysis using JGB
64(6)
2.5.4 How to calculate the principal component analysis?
70(3)
3 Time Series Analysis with R
73(38)
3.1 Preparation of time series data
74(3)
3.2 Before applying for models
77(3)
3.3 The application of the AR model
80(7)
3.3.1 Residual analysis
83(1)
3.3.2 Forecasting
84(3)
3.4 Models extended from AR
87(20)
3.4.1 ARMA and ARIMA model
87(4)
3.4.2 Vector autoregressive
91(6)
3.4.3 GARCH model
97(6)
3.4.4 Co-integration
103(4)
3.5 Application of the time series analysis to finance: Pairs trading
107(4)
SECTION II BASIC THEORY OF FINANCE
4 Modern Portfolio Theory and CAPM
111(18)
4.1 Mean-variance portfolio
113(4)
4.2 Market portfolio
117(3)
4.3 Derivation of CAPM
120(1)
4.4 The extension of CAPM: Multi-factor model
121(4)
4.4.1 Arbitrage Pricing Theory
121(4)
4.4.2 Fama-French's 3 factor model
125(1)
4.5 The form of the efficient frontier
125(4)
5 Interest Rate Swap and Discount Factor
129(10)
5.1 Interest rate swap
129(2)
5.2 Pricing of interest rate swaps and the derivation of discount factors
131(4)
5.3 Valuation of interest rate swaps and their risk
135(4)
6 Discrete Time Model: Tree Model
139(22)
6.1 Single period binomial model
140(9)
6.1.1 Derivative pricing
141(5)
6.1.2 Pricing by risk neutral measure
146(3)
6.2 Multi period binomial model
149(7)
6.2.1 Generalization to the multi period model
149(3)
6.2.2 Pricing call options
152(4)
6.3 Trinomial model
156(5)
7 Continuous Time Model and the Black-Scholes Formula
161(14)
7.1 Continuous rate of return
162(3)
7.2 Ito's lemma
165(2)
7.3 The Black-Scholes formula
167(3)
7.4 Implied volatility
170(5)
SECTION III NUMERICAL METHODS IN FINANCE
8 Monte Carlo Simulation
175(24)
8.1 The basic concept of Monte Carlo simulation
176(3)
8.2 Variance reduction method
179(5)
8.2.1 Antithetic variates method
180(2)
8.2.2 Moment matching method
182(2)
8.3 Exotic options
184(4)
8.4 Multi asset options
188(3)
8.5 Control variates method
191(8)
9 Derivative Pricing with Partial Differential Equations
199(14)
9.1 The explicit method
202(3)
9.2 The implicit method
205(8)
APPENDIX
A Optimization with R
213(8)
A.1 Multi variate optimization problem
213(3)
A.2 The efficient frontier by optimization problem
216(5)
B Noise Reduction via Kalman Filter
221(12)
B.1 Introduction to Kalman filter
222(5)
B.2 Nonlinear Kalman filter
227(6)
C The Other References on R
233(2)
C.1 Information sources on R
233(1)
C.2 R package on finance
234(1)
References 235(10)
Index 245
After finishing a Ph.D course at Kyoto University, Dr. Daisuke Yoshikawa worked for Mizuho-DL financial technology and Bank of Japan. Meanwhile, Dr. Yoshikawa published a few refereed journal papers on finance. Currently, Dr. Yoshikawa is working for Hokkai-Gakuen University as a lecturer.
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