Effective stochastic local volatility models
提出一种有效随机波动率技术，通过半解析近似偏微分方程，实现对随机局部波动率模型中杠杆函数的直接校准，适用于SABR、ZABR或Heston等模型。
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.