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We show the application of an optimal transportation approach to estimatestochastic volatility process by using the flow that optimally transports theset of particles from the prior to a posterior distribution. We also show howto direct the flow to a rarely visited areas of the state space by using aparticle method (a mutation and a reweighing mechanism). We demonstrate theefficiency of our approach on a simple example of the European option priceunder the Stein-Stein stochastic volatility model for which a closed formformula is available. Both homotopy and reweighted homotopy methods show alower variance, root-mean squared errors and a bias compared to other filteringschemes recently developed in the signal-processing literature, includingparticle filter techniques.

Optimal Transport Filtering with Particle Reweighing in Finance