FINANCIAL MATHEMATICS ACTIVITIES

The Fields Institute
Seminar on Financial Mathematics

Wednesday, March 26, 1997, 4:30 - 7:00 p.m.

ABSTRACTS OF THE TALKS

Financial Engineering, General Equilibrium and Transaction Costs
Frank Milne (Queen's University)

I will discuss a research program undertaken by myself, Ted Neave and Xing Jin. We construct a general equilibrium dynamic economy with many agents, commodities and assets. We allow for endogenous transaction costs through a transaction technology. The formulation is suffiently general to include most of the special cases in the literature. First in the paper with Xing Jin, we prove the existence of a competitive equilibrium in this economy, and an approximate equilibrium with non-convex Transaction technologies - the latter allows for fixed costs of transacting. The paper with Neave (work in progress) considers a series of characterisations for asset allocations and asset prices. The model provides a structure which allows financial engineering a real economic role in the economy, and avoids the trivial role for financial engineering in the perfect arbitrage economies of most derivative pricing and hedging models.

Bounds on Option Prices in the Presence of Transaction Costs:
An Explanation of the Implied Volatility Smile
George Constantinides (University of Chicago)

Proportional transaction costs are considered as a possible explanation of the volatility smile of index options. Tight upper and lower bounds on the price of a call option are derived under plausible assumptions about the investors' objectives. The bounds are sufficiently tight to reject the hypothesis that transation costs can account for the volatility smile in an otherwise Black-Scholes market environment.

SPEAKERS

Frank Milne received his Phd in Economics at the Australian National University. He has taught at the University Rochester, ANU and Queen's University, where he is currently Professor of Economics and Finance. He has published extensively in Economic Theory and Finance Theory. Recently he published an introductory graduate text "Finance Theory and Asset Pricing" with OUP.

George Constantinides is the Leo Melamed Professor of Finance at the Graduate School of Business at the University of Chicago and a research associate of the National Bureau of Economic Research. He hold degrees from Oxford University and Indiana University. His research interests are on the valuation of primary and derivative securities. He served as president of the Society for Financial Studies. He is an associate editor of the Journal of Finance, Mathematical Finance, Review of Derivatives Research and European Financial Review. He serves as director, DFA Investment Dimensions Group, Inc., Dimensional Investment Group Inc. and Dimensional Emerging Markets Fund Inc., and trustee, DFA Investment Co.

ORGANIZERS

Claudio Albanese (Professor of Mathematics, University of Toronto), Phelim Boyle (J. Page R. Wadsworth Chair of Finance, University of Waterloo), Don Dawson (Director, The Fields Institute), Ron Dembo (President, Algorithmics Inc.), Gordon Roberts (CIBC Professor of Finance, York University), Stuart Turnbull (Professor of Economics, School of Business, 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 1996-97 Seminar Series on Financial Mathematics is available through electronic notices sent via e-mail and through the Fields Institute's world wide web site.