Computational Finance: Matlab(r) Oriented Modeling

ISBN-13: 9780367492939 / Angielski / Miękka / 2020 / 236 str.

Francesco Cesarone

Opis

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.

Spis treści

Part I Programming techniques for financial calculus 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 2 Preliminary elements in Probability Theory and Statistics 2.1 Basic concepts in probability 2.2 Random variables 2.3 Probability distributions 2.4 Continuous random variables 2.5 Higher-order moments and synthetic indices of a distribution 2.6 Some probability distributions 2.6.1 Uniform distribution 2.6.2 Normal distribution 2.6.3 Log-normal distribution 2.6.4 Chi-square distribution 2.6.5 Student-t distribution 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 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 5 Further elements on Probability Theory and Statistics 5.1 Introduction to Monte Carlo simulation 5.2 Stochastic processes 5.2.1 Brownian motion 5.2.2 Ito’s Lemma 5.2.3 Geometric Brownian motion 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 binomial model 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 the Monte Carlo method 6.3.1 Path Dependent Derivatives References Suggested lesson plan

O autorze

Francesco Cesarone is an Assistant Professor of Computational Finance at the Department of Business Studies of the Roma Tre University, Italy.