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 under a SABR model.