The Fields Institute
Seminar on Financial Mathematics
Wednesday, April 28, 1999, 4:30  7:00 p.m.
SCHEDULE
4:30  5:30 p.m.
"Stochastic Volatility and Separation of Scales"
Ronnie Sircar, University of Michigan
6:00  7:00 p.m.
"Option Valuation with CoIntegrated Asset Prices"
JinChuan Duan, Hong Kong University of Science & Technology
ABSTRACTS OF THE TALKS
"Stochastic Volatility and Separation of Scales"
Ronnie Sircar, Department of Mathematics, University of Michigan.
We present derivative pricing and estimation tools for a class
of stochastic volatility models that exploit the observed "bursty" or persistent
nature of stock price volatility. An empirical analysis of highfrequency
S&P 500 index data confirms that volatility reverts slowly to its mean
in comparison to the tickbytick fluctuations of the index value, but it
is fast meanreverting when looked at over the time scale of a derivative
contract (many months). This motivates an asymptotic analysis of the partial
differential equation satisfied by derivative prices, utilizing the distinction
between these time scales, that yields an explicit formula describing the
geometry of the implied volatility surface across strike prices and expiration
dates. This is used to "fit the skew" from European index option prices. The
theory identifies the three important group parameters that are needed for
derivative pricing and hedging problems. The results considerably simplify
the estimation procedure, and atthemoney Europan call data produces estimates
of the three important parameters which are found to be stable. Other derivatives,
including barriers and Americans, are priced from these three parameters.
Joint work with George Papanicolaou, Department of Mathematics,
Stanford University and JeanPierre Fouque, Department of Mathematics,
North Carolina State University.
"Option Valuation with CoIntegrated Asset Prices"
JinChuan Duan, Hong Kong University of Science & Technology
Many financial data series are found to be cointegrated. The
implications of cointegration on option valuation are studied in this article,
as we develop the option valuation theory for cointegrated price systems.
We also examine the diffusion limit of the system and numerically demonstrate
the cointegration effect using spread options. The consideration of cointegration
is found to yield an option pricing theory that depends on cointegration
premiums if the volatility is stochastic. Our numerical results suggest that
cointegration can substantially alter the value of the spread option.
SPEAKERS
Ronnie Sircar
Education:
 PhD Stanford University 1997
 MS Oxford University 1993
 BA Oxford University 1992
Present position:
 Asst. Prof., Dept. of Mathematics, University of Michigan.

JinChuan Duan is Professor of
Finance and Senior Wei Lun Fellow at the Hong Kong University of Science
and Technology (HKUST). Prior to joining the HKUST in 1996, he was an
associate professor at McGill University. Duan has a Ph.D. in finance
from the University of WisconsinMadison. His research interests cover
derivative security pricing, timeseries econometrics and banking. He
is particularly interested in developing pricing theory and numerical
techniques for timeseries models. His best known work is "The GARCH Option
Pricing Model," published in Mathematical Finance (1995).
ORGANIZERS
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)
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 199899 Seminar Series on Financial Mathematics
is available through electronic notices sent via email and through the
Fields Institute's world wide web site.