Do higher-order realized moments matter for cryptocurrency returns?

Ahmed, Walid M.A.; Mafrachi, Mustafa Al

doi:10.1016/j.iref.2020.12.009

Cited by 24 publications

(12 citation statements)

References 103 publications

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“…If we still believe in the path: kurtosis affects decisions and hence prices, the kurtosis of an asset will have an impact on future returns. Our model provides an easily understood explanation for [51]. A similar observation is [52].…”

Section: Multidimensional Situationsupporting

confidence: 68%

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Asset Pricing Model Based on Fractional Brownian Motion

Yan

Wang

2022

Fractal Fract

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This paper introduces one unique price motion process with fractional Brownian motion. We introduce the imaginary number into the agent’s subjective probability for the reason of convergence; further, the result similar to Ito Lemma is proved. As an application, this result is applied to Merton’s dynamic asset pricing framework. We find that the four order moment of fractional Brownian motion is entered into the agent’s decision-making. The decomposition of variance of economic indexes supports the possibility of the complex number in price movement.

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Section: Multidimensional Situationsupporting

confidence: 68%

“…This result from classical observations supports the results of our model. Ahmed and Al Mafrachi 2021 [51] found that kurtosis has a predictive effect on returns in the cryptocurrency market. In our model investors' decisions are influenced by the kurtosis of an asset.…”

Section: Multidimensional Situationmentioning

confidence: 99%

Asset Pricing Model Based on Fractional Brownian Motion

Yan

Wang

2022

Fractal Fract

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“…Kinateder and Papavassiliou (2019) show that realized fourth moment can predict sovereign bond returns during a crisis. Ahmed and Al Mafrachi (2021) show that realized moments up to the fifth-order can explain cryptocurrency returns.…”

Section: Discussionmentioning

confidence: 93%

“…Recent studies such as Khademalomoom et al (2019), Ahmed and Al Mafrachi (2021) and Cui et al (2022) deal with the first six moments. Accordingly, the first six cumulants κ l ðY Þ are described in the second column of Table 2.…”

Section: Jdqsmentioning

confidence: 99%

“…Kraus and Litzenberger (1976) and Dittmar (2002) demonstrate the relationship between higher-order moments and expected returns, and the concept of the realized variance has been extended to realized higher-order moments. In many studies, including those of Amaya et al (2015), Sim (2016), Kim (2016), Mei et al (2017), Kinateder and Papavassiliou (2019), and Ahmed and Al Mafrachi (2021) [1], a realized kth order moment is defined as a sum of kth orders of sub-periodical returns. However, according to Amaya et al (2015) and Bae and Lee (2021), these conventional realized higher-order moments can reflect neither the volatility of volatility nor cross-period relation among sub-periodical returns and are, therefore, flawed.…”

Section: Introductionmentioning

confidence: 99%

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Geometric and arithmetic realized comoments

Bae

2022

JDQS

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The author investigates realized comoments that overcome the drawback of conventional ones and derive the following findings. First, the author proves that (even generalized) geometric implied lower-order comoments yield neither geometric realized third comoment nor fourth moment. This is in contrast to previous studies that produce geometric realized third moment and arithmetic realized higher-order moments through lower-order implied moments. Second, arithmetic realized joint cumulants are obtained through complete Bell polynomials of lower-order joint cumulants. This study’s realized measures are unbiased estimators and they can, therefore, overcome the drawbacks of conventional realized measures.

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Higher moment connectedness of cryptocurrencies: a time-frequency approach

Nyakurukwa

Seetharam

2023

J Econ Finan

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The purpose of the study is to examine higher moment connectedness among 12 cryptocurrencies using data sampled at the 1-minute high-frequency interval. We use methods that demonstrate the heterogeneity of agents from their distinct investing horizons. This includes wavelet multiple cross-correlations, CEEMDAN-based Diebold-Yilmaz (DY) connectedness index and the Barunik-Krehlik (BK) frequency connectedness index. First, our results show that higher moment multiple correlations among the sampled cryptocurrencies are higher at all time scales and the relationship strengthens at lower frequencies. Second, the wavelet cross-correlations show different cryptocurrencies with the potential to lead and lag in the transmission of higher moment shocks to the whole system at different frequencies. Again, the multiple wavelet cross-correlations increase with increasing time scales. The results from the CEEMDAN-based DY connectedness index as well as the BK framework also reveal cyclical connectedness and differences in connectedness across different frequencies. The results show more connectedness of higher moments than the connectedness empirically reported for returns and volatility. Cryptocurrency connectedness has mostly been examined using the first two moments. We extend this line of literature by examining the third and fourth moments, which might be more useful for risk management purposes.

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Do higher-order realized moments matter for cryptocurrency returns?

Cited by 24 publications

References 103 publications

Asset Pricing Model Based on Fractional Brownian Motion

Asset Pricing Model Based on Fractional Brownian Motion

Geometric and arithmetic realized comoments

Higher moment connectedness of cryptocurrencies: a time-frequency approach

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