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