Computational Finance: MATLAB® Oriented Modeling / Edition 1

by Francesco Cesarone

Overview

Computational finance is increasingly important in the financial industry, as a necessary instrument for applying theoretical models to real-world challenges. Indeed, many models used in practice involve complex mathematical problems, for which an exact or a closed-form solution is not available. Consequently, we need to rely on computational techniques and specific numerical algorithms. This book combines theoretical concepts with practical implementation. Furthermore, the numerical solution of models is exploited, both to enhance the understanding of some mathematical and statistical notions, and to acquire sound programming skills in MATLAB®, which is useful for several other programming languages also. The material assumes the reader has a relatively limited knowledge of mathematics, probability, and statistics. Hence, the book contains a short description of the fundamental tools needed to address the two main fields of quantitative finance: portfolio selection and derivatives pricing. Both fields are developed here, with a particular emphasis on portfolio selection, where the author includes an overview of recent approaches. The book gradually takes the reader from a basic to medium level of expertise by using examples and exercises to simplify the understanding of complex models in finance, giving them the ability to place financial models in a computational setting. The book is ideal for courses focusing on quantitative finance, asset management, mathematical methods for economics and finance, investment banking, and corporate finance.

Product Details

ISBN-13:	9780367492939
Publisher:	Taylor & Francis
Publication date:	08/05/2020
Series:	Routledge-Giappichelli Studies in Business and Management
Pages:	242
Product dimensions:	6.88(w) x 9.69(h) x (d)

About the Author

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

Table of Contents

I Programming techniques for financial calculus 9

1 An introduction to MATLAB®with applications 11

1.1 MATLAB®basics 11

1.1.1 Preliminary elements 12

1.1.2 Vectors and matrices 15

1.1.3 Basic linear algebra operations 18

1.1.4 Element-by-element multiplication and division 21

1.1.5 Colon (:) operator 22

1.1.6 Predefined and user-defined functions 24

1.2 M-file: Scripts and Functions 26

1.3 Programming fundamentals 29

1.3.1 If, else, and elseif construct 29

1.3.2 For loops 32

1.3.3 While loops 33

1.4 MATLAB® graphics 34

1.5 Preliminary exercises on programming 36

1.6 Exercises on the basics of financial evaluation 49

1.6.1 Interest Rate Swap 55

II Portfolio selection 61

2 Preliminary elements in Probability Theory and Statistics 63

2.1 Basic concepts in probability 63

2.2 Random variables 71

2.3 Probability distributions 74

2.4 Continuous random variables 76

2.5 Higher-order moments and synthetic indices of a distribution 80

2.6 Some probability distributions 82

2.6.1 Uniform distribution 83

2.6.2 Normal distribution 86

2.6.3 Log-normal distribution 91

2.6.4 Chi-square distribution 94

2.6.5 Student-t distribution 95

3 Linear and Non-linear Programming 99

3.1 General Framework 99

3.2 Optimization with MATLAB® 100

3.2.1 Linear Programming 101

3.2.2 Quadratic Programming 102

3.2.3 Non-Linear Programming 104

3.3 Multi-objective optimization 106

3.3.1 Efficient solutions and the efficient frontier 108

4 Portfolio Optimization 111

4.1 Portfolio of equities: prices and returns 112

4.2 Risk-return analysis 116

4.2.1 Elements of Expected Utility Theory 116

4.2.2 General Framework 118

4.2.3 Mean-Variance model 119

4.2.4 Effects of diversification for an EW portfolio 139

4.2.5 Mean-Mean Absolute Deviation model 141

4.2.6 Mean-Maximum Loss model 145

4.2.7 Value-at-Risk 149

4.2.8 Mean-Conditional Value-at-Risk model 152

4.2.9 Mean-Gini model 161

4.3 Elements of bond portfolio immunization 166

III Derivatives pricing 175

5 Further elements on Probability Theory and Statistics 177

5.1 Introduction to Monte Carlo simulation 177

5.2 Stochastic processes 179

5.2.1 Brownian motion 187

5.2.2 Ito's Lemma 192

5.2.3 Geometric Brownian motion 196

6 Pricing of derivatives with an underlying security 199

6.1 Binomial model 200

6.1.1 A replicating portfolio of stocks and bonds 201

6.1.2 Calibration of the binomial model 206

6.1.3 Multi-period case 209

6.2 Black-Scholes model 213

6.2.1 Assumptions of the model 214

6.2.2 Pricing of a European call 218

6.2.3 Pricing equation for a call 220

6.2.4 Implied volatility 223

6.2.5 Black-Scholes formulas via integrals 224

6.3 Option Pricing via the Monte Carlo method 226

6.3.1 Path Dependent Derivatives 228

References 231

Suggested lesson plan 235