Calibrating and Pricing with a Stochastic-Local Volatility Model

In this paper, we present our study on using the hybrid stochastic-local volatility (SLV) model for option pricing. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In this paper, we provide detailed discussion on the implementation of the calibration and pricing procedures. The implemented SLV model is used for pricing exotic options in the FX market. Pricing results are presented for the SLV model in direct comparison with the pure local volatility and pure stochastic volatility models. The SLV model is shown to match market traded implied volatility surfaces very well and to improve the pricing accuracy for market traded barrier options