Master's degree in Statistics and Operations Research

Computational Finance. An Introductory Course with R


Course title

Computational Finance. An Introductory Course with R.


Faculty

Argimiro Arratia. Universitat Politècnica de Catalunya, argimiro@cs.upc.edu.

PhD. Mathematics (1997), MSc. Computer Sciences (1993), MA Mathematics (1992) from University of Wisconsin-Madison, USA.

From Sept/2009 to today: Professor/Researcher at Dept. Computer Sciences, Technological University of Catalunya (UPC) Spain.

Jan/2009 - Sept/2009 Visiting Professor at Department of Economics, Carlos III University, Madrid, Spain.

Nov/2003 - Jan/2009 Investigador Ramón y Cajal, associated to the Dept. of Applied Mathematics, University of Valladolid, Spain.

Sept/2001 - April/2003 Research Consultant at INTEVEP-PDVSA. INTEVEP is the Technological Institute of the Venezuelan Oil Company PDVSA.

April/1997 - Sept/2003 Professor/Researcher at Dept of Mathematics, Simón Bolívar University, Caracas, Venezuela.

Chief Editor (2000-2007) of the Boletín de la Asociación Matemática Venezolana,  and currently I am the Series Editor for Atlantis Press and Springer series in “Atlantis Studies in Computational Finance and Financial Engineering”.

Research Interests: Computational Finance, Financial Engineering, Time Series Analysis, Machine Learning, Descriptive Complexity.

 

Course language

English.


Course schedule

June 27 to July 1, from 11:00am to 2:00pm.


Description

Computational Finance includes all numerical methods, all theories of algorithms and optimization heuristics geared to the solutions of problems in economics and finance.

The subject area is broad and requires knowledge in computational statistics, econometrics, mathematical finance and computer science. The aim of this course is to introduce the student in each of these areas from mathematics, statistics and computer sciences that constitute Computational Finance. The course will cover the basics

of financial securities and financial engineering, financial time series models, models for pricing financial derivatives, the Black-Scholes formula, optimization heuristics in finance, and portfolio theory. Details follow.


Course Contents

1: An Abridge Introduction to Finance. Securities (bonds, stocks, options); price and payoff. Stylized empirical facts of asset returns. Arbitrage and risk-neutral valuation. Forecasting. Volatility.

2: Financial Time Series Models. Autoregressive Moving Averages models (ARMA). Nonlinear models: ARCH and GARCH. Nonlinear semi parametric models: Neural Networks, Kernels and Support Vector Machines in financial forecasting and price modeling.

3: Pricing Financial Derivatives. Binomial Tree or CRR model. Brownian motion. Ito's formula. Black-Scholes formula for pricing European options. (If time permits: Monte Carlo simulations of exotic options.)

4: Optimization heuristics in finance. Simulated Annealing, Ant Colony optimization, and other heuristics and their applications to parameter estimation of GARCH and valuing options.

5: Portfolio theory. Markowitz mean-variance portfolio model; Optimization of portfolios under different constraints sets. Portfolio selection.

 

References

[1] A. Arratia, Computational Finance, An Introductory Course with R. Atlantis Press-Springer, 2014.

[2] R. A. Brealey, S. C. Myers, F. Allen. Principles of Corporate Finance, McGraw-Hill, 2011.

[3] P. Brockwell and R. Davies, Introduction to Time Series and Forecasting. Springer, 2002.

[4] J. Hull. Options, Futures and other Derivatives. Prentice-Hall, 2009.

[5] R. Tsay. Analysis of Financial Time Series. Wiley, 2013.

 

Miscelanea

Knowledge of basic statistics and probability theory is necessary. The course includes programming experiments and modeling in R. It is not a prerequisite to know R (although it is desirable), since the necessary background will be given.


Evaluation

Problem assignments which includes theory and programming in R.


Specialization

The course is intended for graduate students in statistics and mathematics, but it is accessible for graduate students in computer science, and business or economics with interest in mathematical finance (and with the required background in statistics and probability).


Classroom

PC2 - June 27 to 30

PC3 - July 1