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