Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it to data. In this paper we present novel Bayesian inference with Gaussian process priors. We obtain a rich representation of the local volatility function with a probabilistic notion of uncertainty attached to the calibrate. We propose an inference algorithm and apply our approach to S&P 500 market data.

翻译：局部波动是一种多用途的备选定价模式,因为其状态取决于扩散系数。 但是,校准是非三重性的,因为它既涉及提出潜在功能的假设模型,也涉及使其适应数据的方法。在本文件中,我们用Gaussian进程前科来介绍新的贝叶斯推论。我们用校准的不确定性的概率概念来获得当地波动功能的丰富代表性。我们提出一种推论算法,并对S & P 500市场数据应用我们的方法。