Optimal Transport Filtering with Particle Reweighing in Finance
Résumé
We propose an optimal transportation approach to price European options under the Stein-Stein stochastic volatility model by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct the flow to a rarely visited areas of the state space by using a particle method (a mutation and a reweighing mechanism). We demonstrate the efficiency of our approach on a simple example for which a closed form formula is available. This method shows lower variance and bias compared to other filtering schemes recently developed in the signal-processing literature, including particle filter techniques.
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