Gaussian Methods for Local Stochastic Volatility

A data-driven and model-free1 approach termed GMMR Hedge or Proxy GMM Hedge has been introduced in Kienitz (2022) and Kienitz (2023). The method uses realizations of stochastic quantities on a discrete time-grid and combines fitted Gaussian Mixture Distributions (GMM), being an established method from statistical learning, with classic analytic techniques based on the properties of the Gaussian distribution. After applying GMMR, a regression method based on Gaussian Mixture Models, to many pricing and hedging problems, we use it for the calibration/simulation of Stochastic Local Volatility models.