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
Organizers:
Phelim Boyle, University of Waterloo
Al Vilcius, CIBC, Toronto
John Chadam, Fields Institute
David Lozinski, Fields Institute
Schedule |
|
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.