Check here for my new paper on Bayesian volatility estimation written with Frank van der Meulen, Moritz Schauer and Peter Spreij. The paper takes a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. A computational algorithm for sampling from the posterior distribution is proposed and its good performance on simulated and real datasets is demonstrated. Bayesian methods have a lot of potential in problems like this one.