ABSTRACT

How do we quantify the impact of making assumptions? How do we value information (data)? How do we capture the interplay between risk (described by a familiar model) and uncertainty (about the model itself)? In this talk I introduce the robust paradigm which strives to answer such questions. The framework is designed to interpolate between model-independent and model-specific settings and to allow to address and quantify the model risk. I explain briefly how classical fundamental notions and theorems in quantitative finance extend to the robust setting. I then focus on simple concrete examples. I use vanilla option prices, together with agent-prescribed bounds on key market characteristics, to drive the interval of no-arbitrage prices and the associated hedging strategies. The setting can be seen as a constrained variant of the classical optimal transportation problem and comes with a natural pricing-hedging duality. I discuss numerical methods based on discretisation and LP implementation but subsequently focus on a deep NN optimisation. Finally, I look at ways to coherently combine option prices data with past time series data, leading to a dynamic robust risk estimation. I explain how such non-parametric statistical estimators of key quantities (e.g., superhedging prices, 10-days V@R) superimposed with option prices can be treated as information signals.

ABOUT THE SPEAKER

Jan Obloj is a Professor of Mathematics and a member of the Mathematical and Computational Finance Group at the Mathematical Institute, Fellow of St John's College, University of Oxford and a member of the Oxford-Man Institute of Quantitative Finance. Before coming to Oxford he was a Marie Curie Post-Doctoral Fellow at Imperial College London. He holds a Ph.D. degree in Mathematics from University Paris VI and Warsaw University.

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