Limits of Multifractal Models for Predicting Asset Prices

Summary

The discussion reviews whether ideas associated with Mandelbrot, including multifractal processes and fractional Brownian motion, have led to useful asset price forecasts. It notes that estimating the Hurst exponent is a key step, but can be difficult. Fractional Brownian motion and stochastic volatility extensions are mentioned as modeling approaches.

The response cautions that fractional Brownian motion does not reproduce important observed return patterns, such as how tails change across time horizons. It characterizes market self similarity as partial rather than complete, and describes multifractal methods as mainly academic, with possible value in foreign exchange. The document provides no specific recent papers, backtests, or forecast performance evidence, so it offers a high level assessment rather than a practical trading method.

Key ideas

• Estimating the Hurst exponent is central to using fractional Brownian motion, but estimation can be difficult.
• Fractional Brownian motion does not match some observed features of financial returns across time horizons.
• Financial markets may show partial self similarity without obeying full multifractal scaling.
• The response characterizes multifractal methods as primarily academic and suggests their practical value may vary by market.

Tags

# Has there been success in applying Mandelbrot's ideas to financial markets?


# Has there been success in applying Mandelbrot's ideas to financial markets?












More specifically, I am looking for recent research papers that have harnessed Mandelbrot's ideas too successfully predict asset prices. I have read many papers about wavelets, and I would like to read what other people (you) consider to be the best work in this field.

Are wavelets the only analyses currently in development that use Mandelbrot's ideas?

Thanks.

## Answer by Quartz (score 6, accepted)

https://quant.stackexchange.com/a/8832

The best known multifractal process is Fractional Brownian Motion. One needs to estimate the Hurst exponent, which can be more tricky than it seems. However the fBM distributional characteristics do not match the main stylised facts, e.g. the thinning of tails for longer horizons, so they are not so much used in practice. There are also extensions accounting for stochastic volatility, leading to a curious hybrid.

Mandelbrot's work has opened an interesting line of research, but its fruits are not so tasty as hoped at first: markets display some self-similarity, but not a full one. After many decades it's still mostly an academic topic. Iirc the only market where multifractals seem to bring something is FX.

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