2017/04/25 by Raphaël Douady, Douady, Raphael, Shohruh Miryusupov +1
Economics, Econometrics and Finance · Environmental Science · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis
paper · pdf · doi:10.48550/arxiv.1704.07698
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.