A Sequential Monte Carlo Approach for the pricing of barrier option in a Stochastic Volatility Model

In this paper we propose a numerical scheme to estimate  the price of a barrier option in a general framework.  More precisely, we extend a classical Sequential  Monte Carlo approach, developed under the hypothesis  of deterministic volatility, to Stochastic Volatility models,  in order to improve the efficiency of Standard Monte Carlo techniques in the case of barrier options whose underlying approaches the barriers. The paper concludes with the  application of our procedure to two case studies in  a SABR model.