Mathematics (Pure and Applied) and Nonlinear Dynamics Colloquium



George C. Papanicolaou



Robert Grimmett Professor in Mathematics, Stanford University



Modeling of Market Volatility




Abstract

The modeling of market volatility is a central issue in financial mathematics, in pricing options, for interest rates, etc. There is no shortage of models, of course, but what is lacking is some rational way of selecting and evaluating models. We will survey briefly some commonly used volatility models, deterministic and stochastic, and we will argue that fast mean reverting stochastic volatility models have many attractive features. One of them is that they do reflect market behavior, for example the SP-500 index volatility. We will explain carefully how this is deduced from the data and its consequences for options pricing.

Thursday, Nov. 12th.
3:30 - 4:30 am
South Hall 6635



Notice change of time and space.



About the Speaker

George C. Papanicolaou is a Robert Grimmett Professor in Mathematics at Stanford University. His fields of specialization include applied and computational mathematics, partial differential equations and stochastic processes. He was an invited plenary speaker at the International Congress of Mathematicians in Berlin 1998, and is usually a plenary speaker at most important meetings in applied mathematics. He is on the editorial board of several journals including the prestigious SIAM Reviews. Papanicolaou is an extremly broad mathematician his current publication list spans fields as diverse as, WAVES IN RANDOM MEDIA, CONVECTION-DIFFUSION, MOTION IN A RANDOM FLOW, NONLINEAR WAVES, ANALYSIS OF MATERIALS, IMPEDANCE TOMOGRAPHY, COMPUTATIONAL METHODS IN MATERIALS, WAVELETS AND PDE'S, SIGNAL ANALYSIS, FLUID MECHANICS, MATHEMATICAL FINANCE and NOISY DYNAMICAL SYSTEMS. It is difficult to find a mathematician pure or applied who is as productive, broad in his interests and universially respected.