Rough volatility via the Lamperti transform

Article Mathematics, Interdisciplinary Applications

Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model

Daniele Angelini et al.

Summary: A Multifractional Process with Random Exponent (MPRE) is used to simulate the dynamics of log-prices in a financial market. It is shown that the Hurst-Holder exponent of the MPRE follows the fractional Ornstein-Uhlenbeck process, which describes the dynamics of the log-volatility in the Fractional Stochastic Volatility Model. Evidence is provided to demonstrate that estimation biases can generate artificial rough volatility in both surrogated and real financial data.

CHAOS SOLITONS & FRACTALS (2023)

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Article Business, Finance

Multiscaling and rough volatility: An empirical investigation

Giuseppe Brandi et al.

Summary: This paper examines the relationship between price multiscaling and volatility roughness, specifically the dependency between the multiscaling features of price time series and the Hurst exponent of the volatility process. Through simulation experiments and real data analysis, it is found that the rough volatility model can reproduce the multiscaling features of price time series when a low Hurst exponent is used, but the results are opposite to those of real data.

INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS (2022)

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Article Business, Finance

Consistent estimation for fractional stochastic volatility model under high-frequency asymptotics

Masaaki Fukasawa et al.

Summary: This study develops a statistical theory for a continuous time approximately log-normal fractional stochastic volatility model, and examines whether the volatility is rough. The study constructs a quasi-likelihood estimator and applies it to realized volatility time series. The empirical study suggests that the tested time series indeed exhibits rough volatility.

MATHEMATICAL FINANCE (2022)

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Article Business, Finance

Decoupling the Short- and Long-Term Behavior of Stochastic Volatility

Mikkel Bennedsen et al.

Summary: The study introduces a new continuous-time model that incorporates roughness and persistence in volatility data. It finds evidence that time series of realized volatility measures exhibit both roughness and high persistence. Through an extensive forecasting study, the models proposed in the article outperform a wide array of benchmarks, indicating the benefits of exploiting roughness and persistence in volatility forecasting.

JOURNAL OF FINANCIAL ECONOMETRICS (2022)

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Article Business, Finance

Volatility has to be rough

Masaaki Fukasawa

Summary: In a viable market, the power-law blow-up of the short ATM skew implies that volatility must be rough.

QUANTITATIVE FINANCE (2021)

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Article Meteorology & Atmospheric Sciences

Testing for differences between two distributions in the presence of serial correlation using the Kolmogorov-Smirnov and Kuiper's tests

John R. Lanzante

Summary: Testing for distributional differences in climate research often involves the KS and KU tests. However, ignoring temporal coherence due to daily autocorrelation in the data can lead to significant inference errors. These errors can be mitigated through effective use of look-up tables or broadly applying polynomial coefficients fit to simulation results.

INTERNATIONAL JOURNAL OF CLIMATOLOGY (2021)

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Article Operations Research & Management Science