Speaker: Bálint Négyesi, Utrecht University
Title: A Deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options
Abstract: Direct financial applications of the methods introduced in Negyesi et al. (2024), Negyesi (2024) are presented. Therein, a new discretization of (discretely reflected) Markovian backward stochastic differential equations is given which involves a Gamma process, corresponding to second-order sensitivities of the associated option’s price. The main contributions of this work is to apply these techniques in the context of portfolio risk management. Large portfolios of a mixture of European and Bermudan derivatives are cast into the framework of discretely reflected BSDEs. The resulting system is solved by a neural network regression Monte Carlo method proposed in the aforementioned papers. Numerical experiments are presented on high-dimensional portfolios, consisting of several European, Bermudan and American options, which demonstrate the robustness and accuracy of the method. The corresponding Profit-and-Loss distributions indicate an order of magnitude gain in the number of rebalancing dates needed in order to achieve a certain level of risk tolerance, when the second-order conditions are also satisfied. The hedging strategies significantly outperform benchmark methods both in the case of standard delta- and delta-gamma hedging.