Abstract:  We develop novel deep learning approaches for pricing European options written on assets that follow jump- or lifted- / rough- diffusion dynamics. The option pricing problem is formulated as a partial (integro-) differential equation, which is approximated via a new implicit-explicit minimizing movement time-stepping approach, involving approximation by deep, residual-type Artificial Neural Networks (ANNs) for each time step. In particular, we split the P(I)DE operator in a symmetric gradient flow with known energy functional and an asymmetric part in which we substitute the neural network of the previous time step, so that we can treat it explicitly. Crucially, the proposed ANN is constructed to ensure the asymptotic behavior of the solution for large values of the underlyings and also leads to consistent outputs with respect to a priori known qualitative properties of the solution. The performance and robustness with respect to the dimension of the methods are assessed in a series of numerical experiments involving the Merton jump-diffusion model and the lifted Heston model. Time permitting we will also discuss convergence results for the proposed schemes.

This is joint work with Emmanuil Georgoulis, Chenguang Liu, Jasper Rou and Costas Smaragdakis.

Bio: Antonis Papapantoleon is a Professor of Mathematical Finance at the Delft Institute of Applied Mathematics, EEMCS, TU Delft and a member of the Delft FinTech Lab. He is also an Affiliated Researcher at the Institute of Applied and Computational Mathematics, FORTH.

Before moving to Delft, he served as an Assistant Professor of Mathematics and Director of FEMO Lab at the School of Applied Mathematical and Physical Sciences, National Technical University of Athens (currently Associate Professor, on leave). He also served as a Junior professor at TU Berlin from 2011 until 2017, and as a Deputy Professor at the University of Mannheim for one semester in 2016–2017. He received his PhD in Mathematics from the University of Freiburg supervised by Ernst Eberlein, and was a post-doc at TU Vienna in the group of Josef Teichmann. His practical experience includes positions at Commerzbank and at the Quantitative Products Laboratory, a joint venture between Deutsche Bank, HU Berlin and TU Berlin.

His research interests range from limit theorems for stochastic systems to the applications of Lévy processes in finance, term structure and LIBOR modeling, systemic risk measurement and management, model-free methods in finance, and applications of machine learning in finance. His research has been published in leading journals of mathematics and mathematical finance, such as The Annals of Applied Probability, Mathematical Finance, Mathematics of Operations Research, Management Science, and the Transactions of the AMS, while he has co-edited a book on Advanced Modelling in Mathematical Finance (Springer, 2016).

His research has been funded by public funding bodies such as the Hellenic Foundation for Research and Innovation, the Europlace Institute of Finance, the DAAD and MATHEON, as well as by private corporations. He has also delivered several invited talks at conferences and seminars around the world.

Meeting Recording: https://ucsb.zoom.us/rec/share/Nj9_zmugF2GbE6WjNidSYT0UxPQuO1lfTFzYJWcIvE5MrlWQbHCQZi3puHn6Qt4S.nc4aihBdhYY5Z7t7

Access Passcode: =1XbB0b@