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# R programming and its applications in financial mathematics

Author: Shuichi Ohsaki; Jori Ruppert-Felsot; Daisuke Yoshikawa Boca Raton : CRC Press, [2018] eBook : Document : EnglishView all editions and formats (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version: Document, Internet resource Internet Resource, Computer File Shuichi Ohsaki; Jori Ruppert-Felsot; Daisuke Yoshikawa Find more information about: Shuichi Ohsaki Jori Ruppert-Felsot Daisuke Yoshikawa 9781315153810 1315153815 9781351649865 1351649868 9781498766104 1498766102 1021173604 1 online resource. Intro; Halftitle Page; Title Page; Copyright; Table of 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 numbers2.3 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 AR3.4.1 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 Meanâ#x80;#x90;variance portfolio; 4.2 Market portfolio; 4.3 Derivation of CAPM; 4.4 The extension of CAPM: Multiâ#x80;#x90;factor model; 4.4.1 Arbitrage Pricing Theory; 4.4.2 Famaâ#x80;#x90;Frenchâ#x80;#x99;s 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 factors5.3 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 Blackâ#x80;#x90;Scholes Formula; 7.1 Continuous rate of return; 7.2 ItÃ ́s lemma; 7.3 The Blackâ#x80;#x90;Scholes formula; 7.4 Implied volatility; SECTION III Numerical Methods in Finance 8 Monte Carlo Simulation8.1 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 Differential Equations; 9.1 The explicit method; 9.2 The implicit method; APPENDIX; Appendix A Optimization with R; A.1 Multi variate optimization problem; A.2 The efficient frontier by optimization problem; Appendix B Noise Reduction via Kalman Filter; B.1 Introduction to Kalman filter; B.2 Nonlinear Kalman filter Shuichi Ohsaki, Jori Ruppert-Felsot, Daisuke Yoshikawa.

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