Probability Section Workshop

GARCH Modeling in Financial Engineering

Bruno Rémillard, HEC, Montréal

June 14, 9:00 am to 4:00 pm


In this workshop, the goal is to present financial engineering applications of GARCH models, including their use for multivariate modeling of dependence through copulas.

First, I will discuss the main properties of GARCH models. Then I will discuss the estimation of parameters using maximum likelihood or quasi maximum likelihood, including recursive computation for the gradient. I will also talk about model verification through tests of goodness-of-fit and tests of serial dependence. Examples of applications to multivariate dependence modeling will be given. In the context of financial engineering, I will also discuss the use of GARCH models in option pricing optimal hedging strategies. Finally, I will present the continuous time approximation by stochastic volatility models of the diffusion.

The material is mostly based on Chapters 7 and 8 of my book "Statistical Methods for Financial Engineering''. R and Matlab programs will be provided.


Bruno Rémillard is Professor of Financial Engineering at HEC Montréal. After completing a Ph.D. in Probability at Carleton University, he was a postdoctoral fellow at Cornell University, before being a professor of Statistics at Université du Québec à Trois-Rivières. He is the author or co-author of more than sixty research articles in Probability, Statistics and Financial Engineering. In 1987, he received the Pierre-Robillard award for the best Ph.D. thesis in Probability and Statistics in Canada and in 2003, he received the prize for the best paper of the year published in the Canadian Journal of Statistics. He was a consultant in the Research and Development group at Innocap, an alternative investment firm located in Montreal, where he mainly helped developing and implanting new quantitative methods for alternative and traditional portfolios. Currently, he is a part-time consultant at the National Bank of Canada.