Estimation of the Volatility Persistence in a Discretly Observed Diffusion Model

Mathieu Rosenbaum
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Mathieu Rosenbaum: Crest

No 2006-02, Working Papers from Center for Research in Economics and Statistics

Abstract: We consider the stochastic volatility model with B a Brownian motion and s of the form where WH is a fractional Brownian motion, independent of the driving Brownian motion B, with Hurst parameter H=1/2. This model allows for persistence in the volatility s. The parameter of interest is H. The functions F, a and f are treated as nuisance parameters and ?0 is a random initial condition. For a fixed objective time T, we construct from discrete data Yi/n,i=0,…,nT, a wavelet based estimator of H, inspired by adaptive estimation of quadratic functionals. We show that the accuracy of our estimator is n-1/(4H+2) and that this rate is optimal in a minimax sense.

Pages: 31
Date: 2006
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