FINANCIAL MATHEMATICS ACTIVITIES

The Fields Institute
Seminar on Financial Mathematics

Wednesday, April 30, 1997, 4:30 - 7:00 p.m.

ABSTRACTS OF THE TALKS

Volatility Clustering, Asymmetry and Hysteresis in Stock Returns
Michel Crouhy (Canadian Imperial Bank of Commerce)

Encompassing a very broad family of ARCH-GARCH models we show that heteroskedasticity, already well documented for the US market, is a worldwide phenomenon. The ATGARCH (1.1) model, where volatility rises more in response to bad news than to good news, and where news are considered bad only below a certain level, is found to be a remarkably robust representation of worldwide stock market returns. The residual structure is then captured by extending ATGARCH (1.1) to a hysteresis model, HGARCH, where we model structured memory effects from past innovations. Obviously, this feature relates to the psychology of the markets and the way traders process information. For the French stock market we show that a shock of either sign may affect volatility differently, depending on the recent past being characterized by either all positive or all negative returns. In the same way a longer term trend of either sign may also influence the impact on volatility of current innovations. It is found that bad news are discounted very quickly in volatility, this effect is reinforced when it comes after a negative trend in the stock index. On the opposite, good news have a very small impact on volatility except when they are clustered over a few days, which in this case reduces volatility substantially.

Pricing Derivatives in the Positive Interest Framework
Bjorn Flesaker (Bear Sterns)

The positive interest framework provides a new representation of the dynamics of the term structure of interest rates. The talk will give an overview of the framework, including its multi-currency version, and discuss the role played by different numeraires and their corresponding martingale measures: the terminal, the risk-neutral, and the natural. Practical issues arising in the context of derivatives pricing, such as state variable representation, numerical implementation, and calibration, will be addressed.

SPEAKERS

Dr. Michel Crouhy is Vice President, Global Analytics, Market Risk Management Division, at Canadian Imperial Bank of Commerce (CIBC). Prior to his current position at CIBC, Crouhy was a Professor of Finance at the HEC School of Management, where he was also Director of the M.S. HEC in International Finance, a unique program which prepares engineers from the best engineering schools in Europe to become investment bankers. He has been a visiting professor at the Wharton School and at UCLA. Crouhy holds a Ph.D. from the Wharton School and is a graduate from Ecole Nationale des Ponts et Chaussées, France.

He has extensively published in academic journals in the areas of banking, options and financial markets, and is editor of the collection Banque & Bourse at Presses Universitaires de France. He is also associate editor of the Journal of Derivatives, the Journal of Banking and Finance, and Financial Engineering and the Japanese Markets. He is a board member of the European Institute for Advanced Studies in Management (EIASM), Brussels. He has also served as a consultant to major financial institutions in Europe and in the United States in the areas of quantitative portfolio management, risk management, valuation and hedging of derivative products, forecasting volatility term structure and correlations.

Bjorn Flesaker is a Managing Director in the Financial Analytics & Structured Transactions Group at Bear Stearns, where he is responsible for all derivatives research and modeling. Previously, he managed the global fixed income derivatives quant group at the Union Bank of Switzerland and the fixed income trading research group at Merrill Lynch. He has a Master of Management degree from the Norwegian School of Management, and he earned a Ph.D. in finance from the University of California at Berkeley in 1990, after which he spent two years as an assistant professor of finance at the University of Illinois at Urbana-Champaign. He has published articles and lectured on a variety of topics in mathematical finance, with particular focus on term structure modeling and derivatives pricing.

ORGANIZERS

Claudio Albanese (Professor of Mathematics, University of Toronto), Phelim Boyle (J. Page R. Wadsworth Chair of Finance, University of Waterloo), Don Dawson (Director, The Fields Institute), Ron Dembo (President, Algorithmics Inc.), Gordon Roberts (CIBC Professor of Finance, York University), Stuart Turnbull (Professor of Economics, School of Business, Queen's University)

OTHER INFORMATION

The Financial Mathematics Seminar is offered to any interested participant -- no reservation is necessary. The Institute is located at 222 College Street, between University Ave. and Spadina Ave. near Huron. Parking is available in pay lots located behind the Fields Institute building (quarters and loonies only), across College St. from the Institute (cash only), and underground at the Clarke Institute of Psychiatry (entry on Spadina Ave., just north of College St.)

Information on the 1996-97 Seminar Series on Financial Mathematics is available through electronic notices sent via e-mail and through the Fields Institute's world wide web site. For quick reference, place an electronic bookmark on the web page