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A multifractal model of asset (in)variances

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  • Grobys, Klaus

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.

Suggested Citation

  • Grobys, Klaus, 2023. "A multifractal model of asset (in)variances," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 85(C).
    • Handle: RePEc:eee:intfin:v:85:y:2023:i:c:s1042443123000355
    DOI: 10.1016/j.intfin.2023.101767
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    More about this item

    Keywords

    Bitcoin; MMAR; Multifractal model of asset invariances; Long memory; Power laws; Hurst exponents;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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