Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance
Abstract
We consider the problem of estimating the roughness of the volatility 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. We provide conditions on the underlying trajectory under which our estimator converges in a strictly pathwise sense. Then we verify that these conditions are satisfied by almost every sample path of fractional Brownian motion (with drift). As a consequence, we obtain strong consistency theorems in the context of a large class of rough volatility models. Numerical simulations show that our estimation procedure performs well after passing to a scale-invariant modification of our estimator.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.02582
- arXiv:
- arXiv:2307.02582
- Bibcode:
- 2023arXiv230702582H
- Keywords:
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- Quantitative Finance - Statistical Finance;
- Mathematics - Probability;
- Mathematics - Statistics Theory