Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, November 18, 2020.

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Wednesday, November 18, 2020

8:30 am in Via Zoom,Wednesday, November 18, 2020

Kriging the local volatility

Matthew Dixon (Illinois Institute of Technology)

Abstract: Gaussian processes (GPs) for option pricing have emerged as novel methodologies for fast computations with applications in risk and delta hedging. However, these approaches do not enforce no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this talk, we develop a finite-dimensional kriging approach for no-arbitrage interpolation of European vanilla option prices which jointly yields the full surface of local volatilities with uncertainty bands, even in the presence of arbitrage in the data. The approach is uniformly asymptotically convergent to a GP in the limit of the grid size. We provide the experimental design parameters that are needed for competitive performance of GPs on a real dataset of SPX vanilla options. Furthermore we demonstrate the performance relative to various popular alternative interpolation techniques including SSVI and no-arbitrage deep learning of implied volatilities. This is joint work with Stéphane Crépey (University of Paris) and Areski Cousin (University of Strasbourg).

Speaker's Biography: Matthew Dixon (FRM) is an Assistant Professor of Applied Math and affiliate in the Stuart Business school who researches applications of machine learning in finance. Matthew began his career as a quant in structured credit trading at Lehman Brothers before consulting for finance and technology firms and pursuing academic research. His Intel funded research has led to new approaches, algorithms and software for fintech with additional funding from the National Science Foundation and Google to develop new technologies for fintech in partnership with the University of Michigan and Northwestern University. In 2020, he released the first textbook on machine learning in finance with Prof. Igor Halperin (NYU and Fidelity Investments). Matthew is also an associate editor of the AIMS Journal of Dynamics and Games and deputy editor of the Journal of Machine Learning in Finance. He has held scientific appointments at Stanford University and UC Davis, and holds a PhD in Applied Math from Imperial College, London, and MS in Comp. Sci. from Reading University, UK.

For meeting info, please email wfchong@illinois.edu

3:00 pm in Zoom,Wednesday, November 18, 2020

Molchanov’s method for small-time heat kernel and bridge asymptotics

Robert Neel (Lehigh University)

Abstract: We discuss a method, going back to work of Molchanov, for determining the small-time asymptotics of the heat kernel at the cut locus of a sub-Riemannian manifold (valid away from any abnormal geodesics), and which provides a systematic approach to a collection of related questions. When the structure of minimal geodesics between two points is known, one can (generally) determine a complete asymptotic expansion for the heat kernel and its derivatives. We describe the possible expansions, in both generic (low-dimensional) cases and non-generic cases. More generally, we give upper and lower bounds, holding uniformly on compacts. Further, we discuss the asymptotics of derivatives of the logarithm of the heat kernel, in particular showing that the (possibly vanishing) leading term is given as a cumulant with respect to a probability measure on the set of minimal geodesics. We give upper bounds on these logarithmic derivatives that hold uniformly on compacts. Returning to the probability measure on minimal geodesics, we show that it also gives the law of large numbers for the associated bridge process. This talk is based on joint work with Davide Barilari, Ugo Boscain, Grégoire Charlot, and Ludovic Sacchelli.

For Zoom info, please email belabbas@illinois.edu