July 17, 2024

The Fields Institute
Seminar on Financial Mathematics

Wednesday, October 29, 1997, 4:30 - 7:00 p.m.

NOTE: The October Meeting will be held at University College, Room #161, 15 King's College Circle (See Map at


4:30 - 5:30 p.m.
Practical Methods of Incorporating Kurtosis and Skewness into VAR measures
and the Pricing and Hedging of Derivatives

Carol Alexander (University of Sussex)

6:00 - 7:00 p.m.
Post-'87 Crash Fears in S&P 500 Futures Options
David Bates (University of Iowa )


Practical Methods of Incorporating Kurtosis and Skewness into VAR
measures and the Pricing and Hedging of Derivatives

Carol Alexander (University of Sussex)

A number of methods for using mixtures of normal distributions to capture 'fat-tailed' and skew financial returns distributions will be discussed. These include JP Morgan's Bayesian approach, and more sophisticated techniques such as neural networks and GARCH. Applications covered range from simple transforms of normal covariance matrices for 'fat-tailed' VAR measures, to pricing and hedging derivatives using term structure forecasts of skewness and kurtosis.

Post-'87 Crash Fears in S&P 500 Futures Options
David Bates (University of Iowa )

This session will discuss the Fourier inversion approach to pricing European options, which permits use of a broader class of distributional hypotheses than have hitherto been considered in the empirical option pricing literature. The approach is illustrated using S&P 500 futures option prices over 1988-93, which have exhibited strongly negatively negatively skewed implicit distributions. Two competing explanations are nested and examined using the Fourier inversion methodology: stochastic volatility models with negative correlations between market levels and volatilities, and negative-mean jump models with time-varying jump frequencies. While volatility and level shocks are substantially negatively correlated, the stochastic volatility model can explain the implicit negative skewness only under extreme parameters (e.g., high volatility of volatility) that are implausible given the time series properties of option prices. The stochastic volatility/jump-diffusion model generates more plausible estimates of volatility processes. Implicit distributions from both models are inconsistent with the absence of large stock index moves over 1988-93.


Carol Alexander
After working in the Mathematics department of the University of Amsterdam, and later as a Bond Analyst for Phillips and Drew (UBS), Carol Alexander joined the Mathematics faculty at the University of Sussex in 1985. Since 1990 she has developed an international reputation for the time-series analysis of financial markets, specialising in risk measurement and investment analysis. In 1996 she moved to a part-time post at the university, when she became the Academic Director of Algorithmics Inc. ( and Editor in Chief of NetExposure, the electronic journal of financial risk (

During the past few years she has been consulting in risk management and time series analysis for banks, corporates and other financial institutions. As a result, most of her academic research work now concentrates on applied financial econometrics, specialising in volatility and correlation analysis. Carol has developed a large number of general and in-house training courses covering the general areas of risk management and investment analysis for financial institutions.

With Algorithmics.Inc. she is developing VAR models for large scale risk management systems and new methods for historical simulation using pattern recognition. Her pattern recognition algorithm, developed with Dr. Ian Giblin (Dept. Mathematics, University of Pisa) won the first international non-linear financial forecasting competition in 1996. She also works with Dr Peter Williams (Dept. Cognitive Science, University of Sussex) on using neural networks to estimate mixtures of normal distributions to model 'fat-tailed' distributions and term structures of kurtosis. Her research on emerging markets includes the analysis of equity and currency derivatives in the Asian-Pacific region, and the hedging of equities with new cointegration software.

She speaks at many international conferences and on mathematical techniques for risk and investment management and has written numerous articles in both academic and professional journals. Carol's books include the edited Handbook of Risk Management and Analysis (First edition April 1996, Second edition in two volumes, forthcoming February 1998, both by Wileys). More details of professional and academic publications are given on

David Bates is an associate professor of finance at the University of Iowa, and a Faculty Research Fellow of the National Bureau of Economic Research. He received his doctorate in economics from Princeton University, and taught at the Wharton School of the University of Pennsylvania from 1988 to 1996. His research primarily involves developing, estimating, and testing option pricing models, with applications to currency and stock index options. His articles have appeared in various academic journals, including the Journal of Finance, Journal of International Money and Finance, and Review of Financial Studies.


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), Gordon Roberts (Finance, York University), and Stuart Turnbull (Economics, Queen's University)


The Financial Mathematics Seminar is offered to any interested participant -- no reservation is necessary.

NOTE: The October Meeting will be held at University College, Room #161, 15 King's College Circle (See Map)

Parking is available along King's College Circle and Hart House Circle, as well as 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 1997-98 Seminar Series on Financial Mathematics is available through electronic notices sent via e-mail and through the Fields Institute's world wide web site.