A Multifractal Model of Asset Returns¶
Mandelbrot, B. B., Fisher, & Calvet, L. (1997). A Multifractal Model of Asset Returns.
Cited by¶
1 citation across 1 artifact.
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Primes¶
- Fractal Geometry
- Ecology and landscape → the set is forest canopy, habitat patches across a landscape, or animal foraging trajectories; the dimension is box-counting on remote-sensing imagery or GPS tracks; the generating principle is approximate (interaction of environmental heterogeneity with biological process); the scale range runs from the smallest resolved patch to the landscape extent; the substrate mechanism is competition, dispersal, fire and disturbance regimes, and human land-use history; the use is conservation planning (habitat connectivity scoring), species-area-relationship calibration, and movement-ecology modeling. Finance and economics → the set is an asset-price time series (in the time-vs-price plane) or the support of large-return events; the dimension is the Hurst exponent for monofractal models or a multifractal spectrum for richer descriptions; the generating principle is statistical (stochastic process with heavy tails and long memory in absolute returns); the scale range runs from sub-second to multi-year; the substrate mechanism is volatility clustering, jump dynamics, and heterogeneous-agent market microstructure; the use, formalized in Mandelbrot, Fisher, and Calvet's (1997) Multifractal Model of Asset Returns, is risk modeling (heavy-tailed VaR), regime detection (multifractal-spectrum shifts as crisis precursors), and option-pricing model selection.
This sourceOriginating formulation of the Multifractal Model of Asset Returns (MMAR), introducing multifractal time-deformation for asset-price scaling (heavy tails, long dependence in absolute returns).
- Ecology and landscape → the set is forest canopy, habitat patches across a landscape, or animal foraging trajectories; the dimension is box-counting on remote-sensing imagery or GPS tracks; the generating principle is approximate (interaction of environmental heterogeneity with biological process); the scale range runs from the smallest resolved patch to the landscape extent; the substrate mechanism is competition, dispersal, fire and disturbance regimes, and human land-use history; the use is conservation planning (habitat connectivity scoring), species-area-relationship calibration, and movement-ecology modeling. Finance and economics → the set is an asset-price time series (in the time-vs-price plane) or the support of large-return events; the dimension is the Hurst exponent for monofractal models or a multifractal spectrum for richer descriptions; the generating principle is statistical (stochastic process with heavy tails and long memory in absolute returns); the scale range runs from sub-second to multi-year; the substrate mechanism is volatility clustering, jump dynamics, and heterogeneous-agent market microstructure; the use, formalized in Mandelbrot, Fisher, and Calvet's (1997) Multifractal Model of Asset Returns, is risk modeling (heavy-tailed VaR), regime detection (multifractal-spectrum shifts as crisis precursors), and option-pricing model selection.
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