The unpredictability of financial markets is on everybody’s mind these days. How can we make educated economic decisions when the appearance of a new influenza strain in Mexico can cause stock prices worldwide to drop significantly within days?

Mathematical modelling is crucial to complex decision making in times of uncertainty, whether for assessing risks or for choosing an optimal course of action. “Over the past ten years, the number of people working in mathematics with applications to the finance industry has increased two to three fold”, says Dr. Matt Davison, leader of the MITACS project Modelling Trading and Risk in the Market.

Dr. Davison is working with 15 scientists and over 50 graduate students and postdoctoral fellows to solve problems relating to debt management, portfolio optimization, interest rates, and credit risk. The models used incorporate a variety of mathematical ideas, including fractional Brownian motion, hidden Markov models, and delay differential equations.

Models of interest to BC Hydro, Ontario Power Generation and the Alberta oil and gas industry have reproduced price spikes in the electricity and natural gas markets. “I’ve observed huge changes within the business in the last 10 years,” says project partner Peter Stabins, President of Dydex Research and Capital. “The deregulation of hydroelectric power has resulted in the need to develop sophisticated models for valuation of electrical options.”

The impact of the project’s work goes beyond modeling risk in financial markets. Graduate student Natasha Kirby has estimated the future value of a corn ethanol plant and is investigating the value of wind power coupled with different storage technologies such as batteries. “Understanding commodity price variations and their impact on green technologies is critical for the future of the environment” says Kirby.

Perhaps most impressive is the breadth of the project. Since its inception ten years ago, the project has grown to include nodes at five Canadian universities and partnerships with 13 companies from the energy, financial software, banking and insurance sectors. Kirby says that the “continued relationship with industry leaders, through programs such as MITACS ACCELERATE, has been crucial to the success of many students.”

And the scope for future work continues to grow. “The bursting of the real estate bubble has opened up a new universe of questions for economists and financial mathematicians,” says Dr. John Walsh, leader of the MITACS Risk and Finance theme. “It is too early to say exactly how the directions will change, but it is clear that they will.”