Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Peter Spreij: Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations

Speaker:

Peter Spreij, University of Amsterdam and Radboud University Nijmegen

 

Abstract: We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation (SDE) driven by a gamma process. The volatility function is assumed to be positive and piecewise constant or Hölder continuous. We first show that the SDE admits a weak solution under a simple growth condition, which is unique in law. In the statistical problem, the volatility function is always modelled a priori as piecewise constant on a partition of the real line, and we specify a gamma prior on its coefficients. This leads to a straightforward procedure for posterior inference. We show that the contraction rate of the posterior distribution is root n (sample size) for piecewise constant volatility and depends on the Hölder exponent in the other case. Joint work with Denis Belomestny, Shota Gugushvili, Moritz Schauer. 

 

 

Note:Face coverings will be required. Even if you are fully vaccinated, all students, staff, faculty, and guests must wear a face covering indoors. The university will review and revise the mask protocol as appropriate given changes to state and city public-health guidelines.

 

Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar