Computation of Robust Option Prices via Martingale Optimal Transport

Abstract: During the last decade there has been a rapid development of methods for computationally addressing optimal transport problems; motivated by applications within robust finance, effort has also been made to generalize some of these techniques to problems equipped with an additional martingale constraint. Computationally solving multi-marginal martingale optimal transport problems remains a challenging task though, particularly for problems formulated with a large number of marginals.

In this talk I will give a brief introduction to the martingale optimal transport problem and motivate why it is interesting from a mathematical finance point of view, before presenting an efficient framework for solving a class of such multi-marginal problems computationally. The method combines the celebrated entropic regularization with the exploitation of certain structures inherent in the problem, enabling fast computation of the optimal dual variables. I will also provide some examples that demonstrates the utility of our method in terms of computing model-independent bounds on the fair price of some exotic options, such as lookback options and Asian options. The talk is based on joint work with Sigrid Källblad and Johan Karlsson.

optimization and controlprobability

Audience: researchers in the discipline

( paper )

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Gothenburg statistics seminar

Series comments: Gothenburg statistics seminar is open to the interested public, everybody is welcome. It usually takes place in MVL14 (http://maps.chalmers.se/#05137ad7-4d34-45e2-9d14-7f970517e2b60, see specific talk). Speakers are asked to prepare material for 35 minutes excluding questions from the audience.

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