June 18, 2024

Financial Mathematics Seminar Series

First Meeting:

4:30 - 7:30 pm, January 25, 1995
Room 2172, Medical Sciences Building
University of Toronto, 1 King's College Circle
Toronto, Ontario


Phelim Boyle, University of Waterloo
Al Vilcius, CIBC, Toronto
John Chadam, Fields Institute
David Lozinski, Fields Institute

4:30 - 5:30

An Integrated Approach to Risk Management
Robert M. Mark, Executive Vice President
Canadian Imperial Bank of Commerce, Toronto
5:30 - 6:00 Refreshments
6:00 - 7:00

The Monte Carlo Method: Some Recent Efficiency Improvements
Phelim Boyle, J. Page R. Wadsworth Chair of Finance
School of Accountancy, University of Waterloo
7:00 - 7:30

Discussion and Upcoming Seminars
John Chadam, President and Scientific Director
Fields Institute

Abstracts of Talks:

An Integrated Approach to Risk Management
Financial Risk Management concepts are presented within an overall business framework. The semantics of dealing with business uncertainty lead naturally to mathematical structures obtained by abstraction, and resulting in the emergence of various statistical objects used in the estimation of both market and credit risk. Consequently, the analysis and synthesis of resulting risk measures lead directly to many important theoretical and practical questions for the management of financial institutions.

The Monte Carlo Method: Some Recent Efficiency Improvements
This paper introduces and illustrates a new version of the Monte Carlo method that has attractive properties for the numerical valuation of derivatives. The traditional Monte Carlo method has proven to be powerful and flexible tool for many types of derivatives calculations. Under the conventional approach pseudo-random numbers are used to evaluate the expression of interest. Unfortunately, the use of pseudo-random numbers yields an error bound that is probabilitic which can be a disadvantage. Another drawback of the standard approach is that many simulations may be required to obtain a high level of accuracy. There are several ways to improve the convergence of the standard method. This paper suggests a new approach which promises to be very useful for applications in finance. Quais-Monte Carlo methods use sequences that are deterministic instead of random. These sequences improve convergence and give rise to deterministic error bounds. The method is explained and illustrated with several examples. These examples include comples derivatives such as basket options, Asian options and energy swaps.