Nonparametric Bayesian volatility learning under microstructure noise

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