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- W4383604369 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." @default.
- W4383604369 created "2023-07-08" @default.
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- W4383604369 date "2023-07-05" @default.
- W4383604369 modified "2023-10-18" @default.
- W4383604369 title "Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance" @default.
- W4383604369 doi "https://doi.org/10.48550/arxiv.2307.02582" @default.
- W4383604369 hasPublicationYear "2023" @default.
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