Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156970 | Stochastic Processes and their Applications | 2008 | 29 Pages |
Abstract
We consider the stochastic volatility model dYt=σtdBt, with BB a Brownian motion and σσ of the form σt=Φ(∫0ta(t,u)dWuH+f(t)ξ0), where WHWH is a fractional Brownian motion, independent of the driving Brownian motion BB, with Hurst parameter H≥1/2H≥1/2. This model allows for persistence in the volatility σσ. The parameter of interest is HH. The functions ΦΦ, aa and ff are treated as nuisance parameters and ξ0ξ0 is a random initial condition. For a fixed objective time TT, we construct from discrete data Yi/n,i=0,…,nTYi/n,i=0,…,nT, a wavelet based estimator of HH, inspired by adaptive estimation of quadratic functionals. We show that the accuracy of our estimator is n−1/(4H+2)n−1/(4H+2) and that this rate is optimal in a minimax sense.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mathieu Rosenbaum,