Π.Μ.Σ στη «Χρηματοοικονομική και Τραπεζική»

## Topics in Quantitative Finance

Full Time// 2nd Semester, Course Code: ΜΕΧΡΗ334

Part Time // 4th Semester, Course Code: ΜΕΧΡΗ-Μ334

Credits: 6

## Learning Outcomes

This course is an introduction to the numerical techniques used widely by applied economists in finance. Its main goal is to bridge the gap between financial theory and computational practice. This is accomplished with the use of the programming language Matlab which is a powerful numerical computing environment for financial applications.

Upon successful completion of the course, the students will be able to

• know and understand the capabilities and functions of the programming language of Matlab.
• develop numerical algorithms in Matlab for pricing financial derivatives and computing their Greek letters with the simulation method of Monte Carlo.
• employ variance reduction techniques for the numerical improvement of simulation methods of random numbers.
• develop numerical lattice algorithms in Matlab for pricing financial derivatives with the method of Binomial Tree.
• construct numerical paths of Geometric Brownian Motion for simulating dynamic risk hedging and pricing path-dependent financial derivatives with the simulation method of Monte Carlo

## General Competences

• Search for, analysis and synthesis of data and information by the use of appropriate technologies.
• Decision-making.
• Individual/Independent work.
• Group/Team work.
• Working in an interdisciplinary environment.
• Introduction of innovative research.
• Critical thinking.
• Development of free, creative and inductive thinking.

## Course Content

The following sections will be presented:

• Introduction to Matlab: Matrices, Basic Functions, Programming (M-files), Diagrams.
• Monte Carlo Simulation: Generating Random Numbers, Expected Value Estimation, Pricing of European Options, Number of Replications.
• Variance Reduction Techniques: Antithetic Sampling, Control Variates, Common Random Numbers – Estimation of the Greeks.
• Binomial Model Simulation: Construction of Binomial Tree, Pricing of European and American Options.
• Simulation of Geometric Brownian Motion: Sources of Errors, Asset Path Generation, Stop-Loss and Delta Hedging Strategies, Pricing of Exotic Options – Asian, Barrier and Lookback Options.

## Student Performance Evaluation

• Project (40%) that includes the development and execution of computational algorithms for pricing and/or hedging financial derivatives.
• Presentation (30%) of the above project.
• Coursework (30%) that includes the development and execution of computational algorithms for the numerical solution of problems, subject to the material taught in class.

## Bibliography

Suggested Bibliography

• Paolo Brandimarte, Numerical Methods in Finance and Economics: A Matlab- Based Introduction, 2nd Edition, John Wiley & Sons, New York, 2006.
• John C. Hall, Options, Futures, And Other Derivatives, 8th Edition, Prentice Hall, New Jersey, 2011.