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

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  • Masaaki Fukasawa
  • Tetsuya Takabatake
  • Rebecca Westphal

Abstract

We develop a statistical theory for a continuous time approximately log‐normal fractional stochastic volatility model to examine whether the volatility is rough, that is, whether the Hurst parameter is less than one half. We construct a quasi‐likelihood estimator and apply it to realized volatility time series. Our quasi‐likelihood is based on the error distribution of the realized volatility 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 its finite sample performance. Our empirical study suggests that the volatility of the time series examined is indeed rough.

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  • Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2022. "Consistent estimation for fractional stochastic volatility model under high‐frequency asymptotics," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1086-1132, October.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:4:p:1086-1132
    DOI: 10.1111/mafi.12354
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    References listed on IDEAS

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    Cited by:

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