Statistical Inference for Fractional Volatility

We consider a statistical inference problem for a continuous-time fractional volatility model based on high frequency observations of a quadratic variation of an asset price. Our contribution is to construct a consistent... [ view full abstract ]

We consider a statistical inference problem for a continuous-time fractional volatility model based on high frequency observations of a quadratic variation of an asset price. Our contribution is to construct a consistent estimator of the Hurst and diffusion parameters in the instantaneous volatility process. In order to take volatility proxy errors into account, we work under a certain noisy observation model derived from a stable convergence theorem for a quadratic variation of a semimartingale. Some empirical results using our estimator are also given, supporting rough volatility models.