FRE Special Seminar: Jean-François Chassagneux

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Jean-François Chassagneux

Professor in the Finance and Insurance group of the CREST at ENSAE Paris

Title

Numerical bounds for European option prices in uncertainty volatility model.

Abstract

In this talk, we discuss how to produce a numerical interval which contains (or approximately contains) the price of an European option under the Uncertain Volatility Model (UVM). The pricing function, in such models, is solution to a fully non-linear Hamilton-Jacobi-Bellman equation.

We first present a numerical method based on stochastic policy gradients for approximating the option price. By construction, this approach provides a lower bound on the true price. For industrial applications, however, this can be unsatisfactory. We therefore construct an upper bound that can also be approximated numerically to provide a computable certificate on the pricing error. The construction is based on PDE residuals and can be interpreted as an a posteriori error estimate.

This talk is based on joint works with L. Abbas-Turki (SU), J.-P. Lemor (BNP), G. Loeper (BNP) and S. Sananes (UPC).

Bio

Jean-François Chassagneux is a Professor in the Finance and Insurance group of the CREST at ENSAE Paris. His research lies at the crossroads of probability theory, numerical analysis, and financial and insurance modelling. His interests include probabilistic methods for nonlinear partial differential equations, the analysis and numerical approximation of backward stochastic differential equations (BSDEs), stochastic control and mean-field models, as well as market modelling in the presence of frictions and imperfections. His work aims to develop robust mathematical frameworks and efficient computational methods to address key challenges in risk management, pricing, and optimization in finance and insurance.