Is Volatility Rough ?

by   Masaaki Fukasawa, et al.

Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter less than half, and have attracted much attention since a seminal paper titled "Volatility is rough" was posted on SSRN in 2014 claiming that they explain a scaling property of realized variance time series. From our point of view, the analysis is not satisfactory because the estimation error of the latent volatility was not taken into account; we show by simulations that it in fact results in a fake scaling property. Motivated by this preliminary finding, we construct a quasi-likelihood estimator for a fractional stochastic volatility model and apply it to realized variance time series to examine whether the volatility is really rough. Our quasi-likelihood is based on a central limit theorem for the realized volatility estimation error and a Whittle-type approximation to the auto-covariance of the log-volatility process. We prove the consistency of our estimator under high frequency asymptotics, and examine by simulations the finite sample performance of our estimator. Our empirical study suggests that the volatility is indeed rough; actually it is even rougher than considered in the literature.


Rough volatility: fact or artefact?

We investigate the statistical evidence for the use of `rough' fractiona...

Roughness in spot variance? A GMM approach for estimation of fractional log-normal stochastic volatility models using realized measures

In this paper, we develop a generalized method of moments approach for j...

Quasi-Likelihood Analysis of Fractional Brownian Motion with Constant Drift under High-Frequency Observations

Consider an estimation of the Hurst parameter H∈(0,1) and the volatility...

Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance

We consider the problem of estimating the roughness of the volatility in...

On the universality of the volatility formation process: when machine learning and rough volatility agree

We train an LSTM network based on a pooled dataset made of hundreds of l...

Deep Hedging under Rough Volatility

We investigate the performance of the Deep Hedging framework under train...

Weak error rates for option pricing under the rough Bergomi model

In quantitative finance, modeling the volatility structure of underlying...

Please sign up or login with your details

Forgot password? Click here to reset