Estimation of the volatility persistence in a discretely observed diffusion model

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Rosenbaum, Mathieu^1,2 

[1] CREST ENSAE, F-92245 Malakoff, France

[2] Univ Paris Est, Lab Anal & Math Appl, UMR CNRS 8050, Paris, France

关键词: stochastic volatility models;    discrete sampling;    high frequency data;    fractional Brownian motion;    scaling exponent;    adaptive estimation of quadratic functionals;    wavelet methods;   

DOI  :  10.1016/j.spa.2007.09.004

来源: Elsevier

【 摘 要 】

We consider the stochastic volatility model dY(t) = sigma(t) dB(t), with B a Brownian motion and a of the form sigma(t) = Phi(integral(t)(0) a(t, u)dW(u)(H) + f (t)xi(0)), where W-H 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 sigma. The parameter of interest is H. The functions Phi, a and f are treated as nuisance parameters and xi(0) is a random initial condition. For a fixed objective time T, we construct from discrete data Y-i/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. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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