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E-raamat: Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R

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  • Ilmumisaeg: 11-Sep-2017
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119388081
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Applied Probabilistic Calculus for Financial Engineering: An Introduction Using RSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Sep-2017
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119388081
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Illustrates how R may be used successfully to solve problems in quantitative finance

Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering—walking the reader through building an effective financial model from the Geometric Brownian Motion (GBM) Model via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed—along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN.

  • Covers optimization methodologies in probabilistic calculus for financial engineering
  • Answers the question: What does a "Random Walk" Financial Theory look like?
  • Covers the GBM Model and the Random Walk Model
  • Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model

Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R s an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.

Preface xiii
1 Introduction to Financial Engineering 1(18)
1.1 What Is Financial Engineering?
1(1)
1.2 The Meaning of the Title of This Book
2(1)
1.3 The Continuing Challenge in Financial Engineering
3(3)
1.3.1 The Volatility of the Financial Market
3(1)
1.3.2 Ongoing Results of the XYZ-LPL Investment of the Account of Mr. and Mrs. Smith
4(2)
1.4 "Financial Engineering 101": Modern Portfolio Theory
6(5)
1.4.1 Modern Portfolio Theory (MPT)
7(1)
1.4.2 Asset Allocation and Portfolio Volatility
7(1)
1.4.3 Characteristic Properties of Mean-Variance Optimization (MVO)
8(3)
1.5 Asset Class Assumptions Modeling
11(3)
1.5.1 Examples of Modeling Asset Classes
11(6)
1.5.1.1 Modeling Asset Classes
11(3)
1.6 Some Typical Examples of Proprietary Investment Funds
14(1)
1.7 The Dow Jones Industrial Average (DJIA) and Inflation
15(2)
1.8 Some Less Commendable Stock Investment Approaches
17(1)
1.8.1 Day Trading
17(1)
1.8.2 Algorithmic Trading
17(1)
1.9 Developing Tools for Financial Engineering Analysis
18(1)
2 Probabilistic Calculus for Modeling Financial Engineering 19(36)
2.1 Introduction to Financial Engineering
19(1)
2.1.1 Some Classical Financial Data
19(1)
2.2 Mathematical Modeling in Financial Engineering
19(5)
2.2.1 A Discrete Model versus a Continuous Model
19(1)
2.2.2 A Deterministic Model versus a Probabilistic Model
20(4)
2.2.2.1 Calculus of the Deterministic Model
20(3)
2.2.2.2 The Geometric Brownian Motion (GBM) Model and the Random Walk Model
23(1)
2.2.2.3 What Does a "Random Walk" Financial Theory Look Like?
23(1)
2.3 Building an Effective Financial Model from GBM via Probabilistic Calculus
24(2)
2.3.1 A Probabilistic Model for the Stock Market
25(1)
2.3.2 Probabilistic Processes for the Stock Market Entities
25(1)
2.3.3 Mathematical Modeling of Stock Prices
26(1)
2.3.4 A Simple Case
26(1)
2.4 A Continuous Financial Model Using Probabilistic Calculus: Stochastic Calculus, Ito Calculus
26(7)
2.4.1 A Brief Observation of the Geometric Brownian Motion
27(1)
2.4.2 Ito Calculus
28(5)
2.4.2.1 The Ito Lemma
28(5)
2.5 A Numerical Study of the Geometric Brownian Motion (GBM) Model and the Random Walk Model Using R
33(22)
2.5.1 Modeling Real Financial Data
33(2)
2.5.1.1 The Geometric Brownian Motion (GBM) Model and the Random Walk Model
33(1)
2.5.1.2 Other Models for Simulating Random Walk Systems Using R
34(1)
2.5.2 Some Typical Numerical Examples of Financial Data Using R
35(20)
3 Classical Mathematical Models in Financial Engineering and Modern Portfolio Theory 55(180)
3.1 An Introduction to the Cost of Money in the Financial Market
55(2)
3.2 Modern Theories of Portfolio Optimization
57(66)
3.2.1 The Markowitz Model of Modern Portfolio Theory (MPT)
57(6)
3.2.1.1 Risk and Expected Return
57(2)
3.2.1.2 Diversification
59(1)
3.2.1.3 Efficient Frontier with No Risk-Free Assets
59(1)
3.2.1.4 The Two Mutual Fund Theorem
60(1)
3.2.1.5 Risk-Free Asset and the Capital Allocation Line
61(1)
3.2.1.6 The Sharpe Ratio
61(1)
3.2.1.7 The Capital Allocation Line (CAL)
61(2)
3.2.1.8 Asset Pricing
63(1)
3.2.1.9 Specific and Systematic Risks
63(1)
3.2.2 Capital Asset Pricing Model (CAPM)
63(3)
3.2.2.1 The Security Characteristic Line (SCL)
65(1)
3.2.3 Some Typical Simple Illustrative Numerical Examples of the Markowitz MPT Using R
66(14)
3.2.3.1 Markowitz MPT Using R: A Simple Example of a Portfolio Consisting of Two Risky Assets
67(9)
3.2.3.2 Evaluating a Portfolio
76(4)
3.2.4 Management of Portfolios Consisting of Two Risky Assets
80(9)
3.2.4.1 The Global Minimum-Variance Portfolio
83(5)
3.2.4.2 Effects of Portfolio Variance on Investment Possibilities
88(1)
3.2.4.3 Introduction to Portfolio Optimization
89(1)
3.2.5 Attractive Portfolios with Risk-Free Assets
89(29)
3.2.5.1 An Attractive Portfolio with a Risk-Free Asset
90(23)
3.2.5.2 The Tangency Portfolio
113(3)
3.2.5.3 Computing for Tangency Portfolios
116(2)
3.2.6 The Mutual Fund Separation Theorem
118(1)
3.2.7 Analyses and Interpretation of Efficient Portfolios
119(4)
3.3 The Black-Litterman Model
123(2)
3.4 The Black-Scholes Option Pricing Model
125(3)
3.4.1 Keep on Modeling!
126(2)
3.5 The Black-Litterman Model
128(52)
3.6 The Black-Litterman Model
180(14)
3.6.1 Derivation of the Black-Litterman Model
180(4)
3.6.1.1 Derivation Using Theirs Mixed Estimation
180(2)
3.6.1.2 Derivation Using Bayes' Theory
182(2)
3.6.2 Further Discussions on The Black-Litterman Model
184(52)
3.6.2.1 An Alternative Formulation of the Black-Litterman Formula
186(1)
3.6.2.2 A Fundamental Relationship: rA N{[ J, (1 + T)>I
187(2)
3.6.2.3 On Implementing the Black-Litterman Model
189(5)
3.7 The Black-Scholes Option Pricing Model
194(15)
3.8 Some Worked Examples
209(26)
4 Data Analysis Using R Programming 235(134)
4.1 Data and Data Processing
236(6)
4.1.1 Introduction
237(5)
4.1.1.1 Coding
237(5)
4.2 Beginning R
242(18)
4.2.1 A First Session Using R
245(12)
4.2.2 The R Environment-This is Important!
257(3)
4.3 R as a Calculator
260(26)
4.3.1 Mathematical Operations Using R
260(1)
4.3.2 Assignment of Values in R and Computations Using Vectors and Matrices
261(1)
4.3.3 Computations in Vectors and Simple Graphics
262(1)
4.3.4 Use of Factors in R Programming
263(2)
4.3.5 Simple Graphics
265(3)
4.3.6 x as Vectors and Matrices in Statistics
268(1)
4.3.7 Some Special Functions that Create Vectors
269(1)
4.3.8 Arrays and Matrices
270(1)
4.3.9 Use of the Dimension Function dim() in R
271(1)
4.3.10 Use of the Matrix Function matrix() In R
271(1)
4.3.11 Some Useful Functions Operating on Matrices in R: Colnames, Rownames, and t (for transpose)
272(1)
4.3.12 NA "Not Available" for Missing Values in Data sets
273(1)
4.3.13 Special Functions That Create Vectors
273(13)
4.4 Using R in Data Analysis in Financial Engineering
286(39)
4.4.1 Entering Data at the R Command Prompt
286(32)
4.4.1.1 Creating a Data Frame for R Computation Using the EXCEL Spreadsheet (on a Windows Platform)
287(2)
4.4.1.2 Obtaining a Data Frame from a Text File
289(2)
4.4.1.3 Data Entry and Analysis Using the Function data.entry()
291(1)
4.4.1.4 Data Entry Using Several Available R Functions
291(2)
4.4.1.5 Data Entry and Analysis Using the Function scan()
293(2)
4.4.1.6 Data Entry and Analysis Using the Function Source()
295(1)
4.4.1.7 Data Entry and Analysis Using the Spreadsheet Interface in R
296(2)
4.4.1.8 Financial Mathematics Using R: The CRAN Package FinancialMath
298(20)
4.4.2 The Function list() and the Construction of data.frame() in R
318(3)
4.4.3 Stock Market Risk Analysis: ES (Expected Shortfall) in the Black-Scholes Model
321(4)
4.5 Univariate, Bivariate, and Multivariate Data Analysis
325(44)
4.5.1 Univariate Data Analysis
325(3)
4.5.2 Bivariate and Multivariate Data Analysis
328(41)
5 Assets Allocation Using R 369(32)
5.1 Risk Aversion and the Assets Allocation Process
369(1)
5.2 Classical Assets Allocation Approaches
370(8)
5.2.1 Going Beyond a and p
371(1)
5.2.2 y Factors
371(5)
5.2.2.1 Measuring y
373(1)
5.2.2.2 How to Measure y
373(3)
5.2.3 The Mortality Model
376(1)
5.2.4 Sensitivity Analysis
377(1)
5.2.4.1 The Elasticity of Intertemporal Substitution (EOIS)
377(1)
5.3 Allocation with Time Varying Risk Aversion
378(4)
5.3.1 Risk Aversion
378(3)
5.3.1.1 Example of a Risk-Averse/Neutral/Loving Investor
378(1)
5.3.1.2 Expected Utility Theory
379(1)
5.3.1.3 Utility Functions
380(1)
5.3.2 Utility of Money
381(1)
5.4 Variable Risk Preference Bias
382(2)
5.4.1 Time-Varying Risk Aversion
383(2)
5.4.1.1 The Rationale Behind Time-Varying Risk Aversion
383(1)
5.4.1.2 Risk Tolerance for Time-Varying Risk Aversion
383(1)
5.5 A Unified Approach for Time Varying Risk Aversion
384(1)
5.6 Assets Allocation Worked Examples
385(16)
5.6.1 Worked Example 1: Assets Allocation Using R
385(5)
5.6.2 Worked Example 2: Assets Allocation Using R, from CRAN
390(3)
5.6.3 Worked Example 3: The Black-Litterman Asset
393(8)
6 Financial Risk Modeling and Portfolio Optimization Using R 401(96)
6.1 Introduction to the Optimization Process
401(2)
6.1.1 Classical Optimization Approach in Mathematics
401(1)
6.1.1.1 Global and Local Optimal Values
401(1)
6.1.1.2 Graphical Illustrations of Global and Local Optimal Value
402(1)
6.1.2 Locating Functional Maxima and Minima
402(1)
6.2 Optimization Methodologies in Probabilistic Calculus for Financial Engineering
403(2)
6.2.1 The Evolutionary Algorithms (EA)
404(1)
6.2.2 The Differential Evolution (DE) Algorithm
404(1)
6.3 Financial Risk Modeling and Portfolio Optimization
405(4)
6.3.1 An Example of a Typical Professional Organization in Wealth Management
405(4)
6.3.1.1 LPL (Linsco Private Ledger) Financial
405(4)
6.4 Portfolio Optimization Using R
409(88)
6.4.1 Portfolio Optimization by Differential Evolution (DE) Using R
409(2)
6.4.2 Portfolio Optimization by Special Numerical Methods
411(1)
6.4.3 Portfolio Optimization by the Black-Litterman Approach Using R
412(22)
6.4.3.1 A Worked Example Portfolio Optimization by the Black-Litterman Approach Using R
413(21)
6.4.4 More Worked Examples of Portfolio Optimization Using R
434(63)
6.4.4.1 Worked Examples of Portfolio Optimization-No. 1 Portfolio Optimization by PerformanceAnalytics in CRAN
434(2)
6.4.4.2 Worked Example for Portfolio Optimization-No. 2 Portfolio Optimization using the R code DEoptim
436(14)
6.4.4.3 Worked Example for Portfolio Optimization-No. 3 Portfolio Optimization Using the R Code PortfolioAnalytics in CRAN
450(7)
6.4.4.4 Worked Example for Portfolio Optimization-Portfolio Optimization by AssetsM in CRAN
457(2)
6.4.4.5 Worked Examples from Pfaff
459(38)
References 497(8)
Index 505
BERTRAM K. C. CHAN, PhD, is Consulting Biostatistician at the Loma Linda University Health, School of Medicine, Loma Linda, CA. Dr. Chan is also Software Development and Forum Lecturer at the School of Public Health, LLUH Department of Biostatistics and Epidemiology.
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