Effective stochastic local volatility models

If a high degree of accuracy and market consistency is required for option pricing, stochastic local volatility models are often the approach of choice. When calibrating these types of models, one of the major challenges lies in the proper fitting of the leverage function. This often requires an optimization procedure in terms of computationally intensive numerical methods, such as Monte Carlo simulation, or methods not well suited to local volatility formulations, such as Fourier transform pricing. In this article, we provide an alternative approach using an effective stochastic volatility technique, which provides an efficient semi-analytical approximation of the PDE for the density function of the underlying. This approach allows efficient direct calibration of the leverage function for a large class of stochastic local volatility models, which includes stochastic volatility models such as the SABR, ZABR or Heston model as the underlying base model. We provide calibration and computational schemes and illustrate our approach using numerical experiments.