July 17, 2024

The Fields Institute
Seminar on Financial Mathematics

Wednesday, May 28, 1997, 4:30 - 7:00 p.m.


4:30 - 5:30
Fractals and Scaling in Finance: Discontinuity, Concentration and Risk
Benoit Mandelbrot (IBM)

6:00 - 7:00 p.m.
Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices
Andrew Lo (Massachusetts Institute of Technology)


Fractals and Scaling in Finance: Discontinuity, Concentration and Risk
Benoit Mandelbrot (IBM)

Prices do not follow Brownian motion: the majority are clearly non-Gaussian and the dependence is unquestionable. The speaker will account for both effects by showing that price variation is "scaling:, i.e. the risks are the same at all time scales between clearly separated "cut-offs". His 1963 model relates to change dominated by non-Gaussianity. His 1965 model relates to change dominated by dependence. His current model accounts for both.

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices
Andrew Lo (Massachusetts Institute of Technology)

Implicit in the prices of traded financial assets are Arrow-Debreu state prices or, in the continuous-state case, the state-price density [SPD]. We construct an estimator for the SPD implicit in option prices and derive an asymptotic sampling theory for this estimator to gauge its accuracy. The SPD estimator provides an arbitrage-free method of pricing new, more complex, or less liquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility ``smiles'' for option prices. We perform Monte Carlo simulation experiments to show that the SPD estimator can be successfully extracted from option prices and we present an empirical application using S&P 500 index options.


Benoit Mandelbrot
Abraham Robinson Professor of Mathematical Sciences at Yale University. IBM Fellow Emeritus, T. J. Watson Research Center. Wolf Prize for Physics, 1993. Foreign Associates, U.S. National Academy, Science.

Andrew W. Lo is currently the Harris & Harris Group Professor of Finance at MIT's Sloan School of Management and the director of MIT's Laboratory for Financial Engineering. He received his Ph.D. in economics from Harvard University in 1984, and taught at the University of Pennsylvania's Wharton School as the W.P. Carey Assistant Professor of Finance from 1984 to 1987, and as the W.P. Carey Associate Professor of Finance from 1987 to 1988. His research interests include the empirical validation and implementation of financial asset pricing models; the pricing of options and other derivative securities; financial engineering and risk management; trading technology and market microstructure; statistical methods and stochastic processes; computer algorithms and numerical methods; financial visualization; and, most recently, nonlinear models of stock and bond returns based on neural networks and other nonparametric techniques. He has published numerous articles in finance and economics journals, and is currently an associate editor of the Journal of Portfolio Management and the Annals of Applied Probablility. His recent awards include the Batterymarch, Olin, and Alfred P. Sloan Foundation Fellowships, the American Association for Individual Investors Award, and awards for teaching excellence from both Wharton and MIT.


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)


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.