Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance
从积分方差的离散观测估计随机波动率的粗糙指数
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that measures the so-called roughness exponent of a continuous trajectory, based on discrete observations of its antiderivative. The estimator has a very simple form and can be computed with great efficiency on large data sets. It is not derived…