A Hybrid Stochastic Volatility Model Incorporating Local Volatility

Abstract

In this paper, we present our study on a hybrid stochastic volatility model incorporating local volatility for pricing options in the foreign exchange (FX) market. The hybrid stochastic-local volatility model (SLV) could match the implied volatility surface well and meanwhile shows the flexibility for pricing exotic options. The difficulty in implementing the SLV model lies in the calibration of the leverage function, which can be roughly seen as a ratio between the local volatility and the conditional expectation of stochastic volatility. We will illustrate our implementation of the SLV model and show the pricing performance for exotic options.

Keywords: implied volatility, local volatility, stochastic-local volatility, leverage function

JEL Classification: C6, D4, G12