References for Multifractal Asset-Return Simulation and Correlation

Summary

The document addresses research references for generating asset-return paths with multifractal models, including the question of modeling dependence between assets. The question contrasts this aim with geometric Brownian motion, where normally distributed returns make covariance-based correlation straightforward, and notes interest in multifractal models beyond volatility forecasting.

The accepted response points to a 1997 paper by Mandelbrot, Fisher, and Calvet, specifically its section on constructing multifractal processes. Another answer names a book by Calvet and Fisher as a standard reference on multifractal volatility, forecasting, and pricing. These citations indicate where to investigate process construction, but the document itself gives no algorithm, derivation, empirical comparison, or procedure for generating correlated paths. It therefore serves primarily as a bibliography lead, and readers would need to consult the cited works to assess specific dependence methods and their limitations.

Key ideas

• The question concerns multifractal sample-path generation and dependence across assets.
• A cited 1997 paper discusses multifractal process construction.
• A book by Calvet and Fisher is offered as a broader reference on multifractal volatility and pricing.
• The document points to sources but does not describe a correlation-generation method.

Tags

# Multifractal Model, Generating Sample Paths with Correlations between Assets


# Multifractal Model, Generating Sample Paths with Correlations between Assets












I have studied option pricing using Geometric Brownian Motion to generate sample paths. Because of the normal distribution, it is easy to create a covariance matrix and get correlated asset returns.

I am interested in learning more about Mandelbrot's Multi Fractal model of asset returns and it's applications. From what I can find, there exist much work about forecasting volatility using the multi fractal model.

For my purposes, I am more interested in being able to generate sample paths, i.e. produce time series data. Further I would be interested in somehow modeling correlation between assets.

Does there exist papers dealing with these problems from the viewpoint of the multi fractal model of asset returns?

## Answer by user1157 (score 4, accepted)

https://quant.stackexchange.com/a/9879

The paper "A Multifractal Model of Asset Returns" by B. Mandelbrot, A. Fisher and L. Calvet (1997) discusses the creation of multifractal processes in Section 3.4.

## Answer by vanguard2k (score 4)

https://quant.stackexchange.com/a/9880

Not acutally a paper, but there is even a book on Multifractal Models. It is, to my knowledge, the standard reference on this topic by Calvet and Fisher:

Multifractal Volatility: Theory, Forecasting, and Pricing (Academic Press Advanced Finance)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.