Fractional Brownian markets with time-varying volatility and high-frequency data

Lahiri, Ananya; Sen, Rituparna

doi:10.1016/j.ecosta.2018.10.004

Cited by 6 publications

(4 citation statements)

References 22 publications

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“…However, it has not been lost on experts working in this area that the estimation results in the previous literature on long-range dependence in volatility, which pointed out towards Hurst exponents H > 0.5 (and around 0.55) [2,7,20] seem to contradict the claims in the recent 'rough volatility' literature, which points to values of H much smaller than 0.5 (closer to 0.1). Together with the well-known statistical issues plaguing the estimation of Hurst exponents [4,25], these conflicting results call for a critical examination of the empirical evidence for 'rough volatility'.…”

mentioning

confidence: 83%

“…where B H is a fractional Brownian motion (fBM) with Hurst exponent H. This long-range dependence in volatility is modelled by choosing 1 > H > 1/2 [7,5,6,18,20].…”

mentioning

confidence: 99%

“…Compounding this issue is the fact that (spot) volatility is not directly observed but estimated from data with an inherent estimation error, known in the context of high-frequency data as 'microstructure noise', which has been the subject of many studies [3,19,20]. This microstructure noise is far from IID: it is known to possess path-dependent features [19].…”

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confidence: 99%

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Rough volatility: fact or artefact?

Cont¹,

Das²

2022

Preprint

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We investigate the statistical evidence for the use of 'rough' fractional processes with Hurst exponent H < 0.5 for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on discrete sample, using the concept of normalized p-th variation along a sequence of partitions. We investigate the finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes using detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits 'rough' behaviour with an apparent Hurst index H < 0.5. These results suggest that the origin of the roughness observed in realized volatility time-series lies in the microstructure noise rather than the volatility process itself.

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mentioning

confidence: 83%

“…where B H is a fractional Brownian motion (fBM) with Hurst exponent H. This long-range dependence in volatility is modelled by choosing 1 > H > 1/2 [7,5,6,18,20].…”

mentioning

confidence: 99%

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Rough volatility: fact or artefact?

Cont¹,

Das²

2022

Preprint

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“…Hence, if the volatility is driven by fractional Brownian motion, a Hurst index smaller than 1 2 would seem to contradict the market long-range dependent volatility (volatility clustering) [11] [12]. The way the realized volatility is measured at high frequency has however been criticized by several authors [13] [14] [15] suggesting that the origin of the roughness lies in the microstructure noise [16] rather than on the actual volatility process.…”

Section: Rough Volatilitymentioning

confidence: 99%

The fractional volatility model and rough volatility

Mendes¹

2022

Preprint

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Rough Volatility: Fact or Artefact?

Cont,

Das

2024

Sankhya B

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We investigate the statistical evidence for the use of ‘rough’ fractional processes with Hurst exponent $$H< 0.5$$ H < 0.5 for modeling the volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on discrete sample, using the concept of normalized p-th variation along a sequence of partitions. Detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes reveal good finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits ‘rough’ behaviour with an apparent Hurst index $$\widehat{H}<0.5$$ H ^ < 0.5 . These results suggest that the origin of the roughness observed in realized volatility time series lies in the estimation error rather than the volatility process itself.

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Fractional Brownian markets with time-varying volatility and high-frequency data

Cited by 6 publications

References 22 publications

Rough volatility: fact or artefact?

Rough volatility: fact or artefact?

The fractional volatility model and rough volatility

Rough Volatility: Fact or Artefact?

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