A multifractal model of asset (in)variances

Klaus Grobys

Journal of International Financial Markets, Institutions and Money, 2023, vol. 85, issue C

Abstract: This study extends Mandelbrot’s (2008) multifractal model of asset returns to model realized variances across different time frequencies. In a comparative manner, various degrees of time deformations are explored for implementation of the multiplicative cascade. In doing so, this study focuses on two effects: discontinuity measured by the specific power-law exponent and dependency measured by the Hurst exponent. This study shows that the benchmark model, for which Mandelbrot’s (2008) “cartoon” is the foundation, has some remarkable properties as it is capable of explaining the realized variances for the GBP/USD exchange rate and Bitcoin. Notably, the realized variances for crude oil and the S&P 500 require a more extreme time deformation. The invariance hypothesis is confirmed for all realized variances because the power-law exponents for weekly and monthly data coincide with predictions of the multifractal model. Overall, the novel results derived from the proposed multifractal models suggest that some realized variances of otherwise unrelated asset markets are driven by the same underlying “driving force”—a common multifractal cascade.

Keywords: Bitcoin; MMAR; Multifractal model of asset invariances; Long memory; Power laws; Hurst exponents (search for similar items in EconPapers)
JEL-codes: C14 C22 C60 G10 G17 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:intfin:v:85:y:2023:i:c:s1042443123000355

DOI: 10.1016/j.intfin.2023.101767

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