We show the application of an optimal transportation approach to estimate
stochastic volatility process 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 of the European option price
under the Stein-Stein stochastic volatility model for which a closed form
formula is available. Both homotopy and reweighted homotopy methods show a
lower variance, root-mean squared errors and a bias compared to other filtering
schemes recently developed in the signal-processing literature, including
particle filter techniques