Mathematisches Seminar

Prof. Dr. Markus Bibinger, Philipps-Universität Marburg: "Volatility estimation for stochastic PDEs using high-frequency observations (joint work with Mathias Trabs)"

06.07.2017 von 10:15 bis 11:45

LMS 4 - Raum 526 - Übungsraum

Abstract:  We study the parameter estimation for parabolic, linear, second order, stochastic partial differential equations observing a mild solution on a discrete grid in time and space. The SPDE model covers many interesting applications, including the stochastic heat equation and the cable equation in neurobiology. Our main focus is on an application for term structure models.
A high-frequency asymptotic regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide a simple and easy to implement method of moments estimator based on squared increments of the process. The estimator is consistent and admits a central limit theorem. The theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in simulations.

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