Title: Nonparametric Bayesian volatility learning under microstructure noise,
Abstract: Aiming at financial applications, we study the problem of learning the
volatility under market microstructure noise. Specifically, we consider noisy
discrete time observations from a stochastic differential equation and develop
a novel computational method to learn the diffusion coefficient of the
equation. We take a nonparametric Bayesian approach, where we model the
volatility function a priori as piecewise constant. Its prior is specified via
the inverse Gamma Markov chain. Sampling from the posterior is accomplished by
incorporating the Forward Filtering Backward Simulation algorithm in the Gibbs
sampler. Good performance of the method is demonstrated on two representative
synthetic data examples. Finally, we apply the method on the EUR/USD exchange
rate dataset.