Computational Finance : MATLAB® Oriented Modeling.

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Part I: Programming techniques for financial calculus -- Chapter 1: An introduction to MATLAB®with applications -- 1.1: MATLAB®basics -- 1.1.1: Preliminary elements -- 1.1.2: Vectors and matrices -- 1.1.3: Basic linear algebra operations -- 1.1.4: Element-by-element multiplication and division -- 1.1.5: Colon (:) operator -- 1.1.6: Predefined and user-defined functions -- 1.2: M-file: Scripts and Functions -- 1.3: Programming fundamentals -- 1.3.1: if, else, and elseif construct -- 1.3.2: for loops -- 1.3.3: while loops -- 1.4: MATLAB®graphics -- 1.5: Preliminary exercises on programming -- 1.6: Exercises on the basics of financial evaluation -- 1.6.1: Interest Rate Swap -- Part II: Portfolio selection -- Chapter 2: Preliminary elements in Probability Theory and Statistics -- 2.1: Basic concepts in probability -- 2.2: Randomvariables -- 2.3: Probability distributions -- 2.4: Continuous randomvariables -- 2.5: Higher-order moments and synthetic indices of a distribution -- 2.6: Some probability distributions -- 2.6.1: Uniformdistribution -- 2.6.2: Normal distribution -- 2.6.3: Log-normal distribution -- 2.6.4: Chi-square distribution -- 2.6.5: Student-t distribution -- Chapter 3: Linear and Non-linear Programming -- 3.1: General Framework -- 3.2: Optimization with MATLAB® -- 3.2.1: Linear Programming -- 3.2.2: Quadratic Programming -- 3.2.3: Non-Linear Programming -- 3.3: Multi-objective optimization -- 3.3.1: Efficient solutions and the efficient frontier -- Chapter 4: Portfolio Optimization -- 4.1: Portfolio of equities: prices and returns -- 4.2: Risk-return analysis -- 4.2.1: Elements of Expected Utility Theory -- 4.2.2: General Framework -- 4.2.3: Mean-Variance model -- 4.2.4: Effects of diversification for an EW portfolio.

4.2.5: Mean-Mean Absolute Deviation model -- 4.2.6: Mean-Maximum Loss model -- 4.2.7: Value-at-Risk -- 4.2.8: Mean-Conditional Value-at-Risk model -- 4.2.9: Mean-Gini model -- 4.3: Elements of bond portfolio immunization -- Part III: Derivatives pricing -- Chapter 5: Further elements on Probability Theory and Statistics -- 5.1: Introduction toMonte Carlo simulation -- 5.2: Stochastic processes -- 5.2.1: Brownian motion -- 5.2.2: Ito's Lemma -- 5.2.3: Geometric Brownian motion -- Chapter 6: Pricing of derivatives with an underlying security -- 6.1: Binomial model -- 6.1.1: A replicating portfolio of stocks and bonds -- 6.1.2: Calibration of the binomialmodel -- 6.1.3: Multi-period case -- 6.2: Black-Scholes model -- 6.2.1: Assumptions of the model -- 6.2.2: Pricing of a European call -- 6.2.3: Pricing equation for a call -- 6.2.4: Implied volatility -- 6.2.5: Black-Scholes formulas via integrals -- 6.3: Option Pricing via theMonte Carlomethod -- 6.3.1: Path Dependent Derivatives -- References -- Suggested lesson plan.

The theoretical aspects of the book are based on an essential introduction to the building blocks of the two topics under consideration: mathematical programming and stochastic processes. It also includes a primer on MATLAB, as a tool to help students, scholars and practitioners use the concepts in the book.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.