Further Information
The main focus of this talk will be a nonparametric approach for local volatility. We look at the calibration problem in a probabilistic framework based on Gaussian process priors. This gives a way of encoding prior believes about the local volatility function and a model which is flexible yet not prone to overfitting. Besides providing a method for calibrating a (range of) point-estimate(s), we draw posterior inference from the distribution over local volatility. This leads to a principled understanding of uncertainty attached with the calibration. Further, we seek to infer dynamical properties of local volatility by augmenting the input space with a time dimension. Ideally, this provides predictive distributions not only locally, but also for entire surfaces forward in time. We apply our approach to S&P 500 market data.
In the final part of the talk we will give a short account of a nonparametric approach to modelling realised volatility. Again we take a probabilistic view and formulate a hypothesis space of stationary processes for volatility based on Gaussian processes. We demonstrate on the S&P 500 index.