The Fields Institute
Seminar on Financial Mathematics
Wednesday, October 28, 1998, 4:30 - 7:00 p.m.
4:30 - 5:30 p.m.
"Option Pricing Under GARCH Like Processes"
Peter Ritchken, Case Western Reserve University
6:00 - 7:00 p.m.
"Forecasting Exchange Rate Crises with an Application to the Asian Currency
Vance Lindsay Martin, University of Melbourne
ABSTRACTS OF THE TALKS
"Option Pricing Under GARCH Like Processes"
While the theory of pricing options under fairly general GARCH
processes is now well understood, the design of efficient numerical procedures
for pricing them has been lacking. In this seminar we develop efficient lattice
algorithms for pricing European and American options under discrete time GARCH
processes. These algorithms are then extended to price options under generalized
GARCH processes, which contain many of the existing bivariate diffusion models
as limiting cases. We establish one unifying algorithm that is able to price
options under almost all existing GARCH specifications as well as under a
very large family of bivariate diffusions in which volatility follows its
own, perhaps correlated, process.
We also investigate bi-directional regime switching models for
option pricing. Here underlying prices remain in one volatility regime for
a random amount of time before switching over into a new regime. Our family
includes the regime switching models of Hamilton~(1989), in which volatility
influences returns. In addition, our models allow for feedback effects from
returns to volatilities. Our family also includes GARCH option models as a
special limiting case. Our models are more general than GARCH models in that
our variance updating schemes do not only depend on levels of volatility and
asset innovations, but also allow for a second factor that is orthogonal to
Time permitting, we also will investigate GARCH option models
for interest rate claims. Models, like the CIR model, are generalized to incorporate
"Forecasting Exchange Rate Crises with an Application to
the Asian Currency Meltdown"
Vance Lindsay Martin, University of Melbourne (with G. C. Lim)
Standard forecasting models focus on the mean of the distribution
as the point forecast. For markets characterised by diversity of opinions,
especially in the event of a currency crisis, this criterion is inappropriate.
This talk investigates an alternative, more appropriate criterion for forecasting
large changes in exchange rates which highlights the multimodal features of
the underlying distribution. To illustrate the methodology, a model of the
recent Asian currency meltdown is specified and estimated. The results show
evidence of bimodality, in exchange rates, weeks prior to the actual collapse.
These reults are in contrast to standard linear forecasting models.
Peter Ritchken is the Walter Haber
Professor of Finance in the Weatherhead School of Management at Case Western
Reserve University in Cleveland. He has written textbooks on derivatives,
is an editor of Advances in Futures and Options Research, and has published
extensively in the derivatives area. He consults with large investment banks
and brokerage firms, and has conducted executive education programs in the
US, Europe, Asia and Australia. His current research interests are in pricing
interest rate claims, implementing stochastic volatility option models, solving
real option problems, and banking regulation issues. Peter Ritchken received
his PhD in Operations Research from Case Western Reserve University.
Vance L. Martin is currently in the
Economics Department at the University of Melbourne, Australia. He graduated
from Monash University, Australia in 1990 with a PhD in Mathematics. The main
focus of research consists of developing a new class of distributional models,
referred to as generalized exponential distributions, for building and estimating
stochastic non-linear models in economics and finance. Key papers are in the
Journal of the American Statistical Association, Journal of Time Series
Analysis, Journal of Income Distribution, Oxford Bulletin of Economics and
Statistics, Macrodynamics and Journal of International Economics.
The main focus of the applied work has been in identifying multiple
equilibria in economic and financial processes. Many extensions of this work
are contained in two books entitled, Chaos and Non-linear Models in Economics:
Theory and Applications and Nonlinear Models in Economics: Cross-sectional,
Time Series and Neural Network Applications, which have been co-edited
with John Creedy. Current extensions consist of developig new models of risk
which incorporate higher order moments.
Another line of research consists of formulating and estimating
factor models in econometrics. More recently, simulation methods are used
to estimate a range of factor models which special attention is given to term
structure and business cycle models. Some of this work is published in the
Handbook of Statistics.
Claudio Albanese (Mathematics, University of Toronto), Phelim Boyle (Finance,
University of Waterloo), Michel Crouhy (Canadian Imperial Bank of Commerce),
Donald A. Dawson (Fields Institute), Ron Dembo (President, Algorithmics Inc.),
Thomas McCurdy (Management, University of Toronto), Eli Prisman (Finance,
York University), and Stuart Turnbull (Economics, Queen's University)
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 1998-99 Seminar Series on Financial Mathematics is available
through electronic notices sent via e-mail and through the Fields Institute's
world wide web site.