FINANCIAL MATHEMATICS SEMINAR

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 Co-Integrated Asset Prices"
Jin-Chuan Duan, Hong Kong University of Science & Technology

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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 high-frequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparison to the tick-by-tick fluctuations of the index value, but it is fast mean-reverting 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 at-the-money 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 Jean-Pierre Fouque, Department of Mathematics, North Carolina State University.

"Option Valuation with Co-Integrated Asset Prices"
Jin-Chuan Duan, Hong Kong University of Science & Technology

Many financial data series are found to be co-integrated. The implications of co-integration on option valuation are studied in this article, as we develop the option valuation theory for co-integrated price systems. We also examine the diffusion limit of the system and numerically demonstrate the co-integration effect using spread options. The consideration of co-integration is found to yield an option pricing theory that depends on co-integration premiums if the volatility is stochastic. Our numerical results suggest that co-integration can substantially alter the value of the spread option.

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SPEAKERS

Ronnie Sircar
Education:

• Jin-Chuan 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 Wisconsin-Madison. His research interests cover derivative security pricing, time-series econometrics and banking. He is particularly interested in developing pricing theory and numerical techniques for time-series 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 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.