Pricing Window Barrier Options with a Hybrid Stochastic-Local Volatility Model

Abstract

In this paper, we present our research on pricing window barrier options under a hybrid stochastic-local volatility (SLV) model in the foreign exchange (FX) market. Due to the hybrid effect of the local volatility and stochastic volatility components of the model, the SLV model can reproduce the market implied volatility surface, and can improve the pricing accuracy for exotic options at the same time. In this paper, numerical techniques such as Monte Carlo and finite difference methods for standard exotic barrier options under the SLV model are extended to pricing window barrier options and numerical results produced by the SLV model are used to examine the performance and accuracy of the model for pricing window barrier options.

Keywords: stochastic-local volatility, leverage function, window barrier, Monte Carlo, finite difference

JEL Classification: C6, D4, G12