LJKProbability & Statistics Seminar

On Thursday January 19 2017 at 14h00 in Room 106  IMAG Building

Seminary of Paolo PIGATO (Université de Lorraine)

Statistical estimation of the Oscillating Brownian Motion

Summary

The Oscillating Brownian Motion is a classical, simple example of stochastic differential equation with discontinuous diffusion coefficient. It behaves like a Brownian motion which changes variance parameter each time it crosses a certain threshold. We consider here the problem of estimating the parameters of such process from discrete observations. Using some techniques based on approximations of quadratic variation and local time, we propose an estimator for which we prove consistence and a central limit theorem giving the rate of convergence. We consider some application to volatility modeling, being the Oscillating Brownian Motion a simple way to account of volatility clustering and leverage effect. We compare our empirical results with other regime switching models.
(Joint work with Antoine Lejay)
