July 24, 2024

Financial Mathematics Seminars - March 28, 2001

4:30 - 5:30 p.m.

Pricing in Markets Driven by General Processes with Independent Increments

Tom Hurd, McMaster University

Models with stochastic volatility and heavy-tailed noise lead to the theory of pricing in incomplete markets. In this talk we review some of the abundant new results in this direction and work towards a practical and flexible theory which encompasses generalized models of this type. By means of specific examples which illustrate mathematical techniques involving portfolio theory, convex analysis, processes with independent increments, and the Hamilton-Jacobi-Bellman equation, we will try to arrive at a broader view of the problems of modelling in a non-Black-Scholes setting.

Download slides from the talk here.

6:00 - 7:00 p.m.

Dynamic Conditional Correlations

Robert Engle, Stern School of Business, New York University

Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of returns. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and give sensible empirical results.