Kriging the Local Volatility

Fall 2020 Actuarial Science and Financial Mathematics Seminar

Date and Time: Wednesday, November 18, 2020, 8:30 AM (CST)

Speaker: 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.