Chaos Theory, Fractal Returns, and Risk in Quantitative Finance

# Successfull applications of Chaos Theory in Quant Finance


# Successfull applications of Chaos Theory in Quant Finance












Do successful applications of chaos theory to quant finance exist ?

While still in the university I remember some people mentioning how chaos theory and fractals could be applied in a finance context.

The topic has kind of escaped my radar until now. Usually I am quite skeptical when it comes to the application of new research to quant finance. Often the added value isn’t significant but the increase in complexity is. It starts with some famous researching mentioning how some purely theoretical concept might be applied e.g. in pricing derivatives. This precipitates a small landslide of academic research (mostly done by PhD students). After a while people in finance notice those ideas and try first implementations which then show the added benefit to be only marginal.

> As I seet it generally two aspects of chaos theory could be suited for a financial application: spontaneous order (might be used to model how market prices come to pass) distinguishing between random and chaotic data (might be usefuly when dealing with financial time series)

Some references that I personally find interesting:

- Chaos in Economics and Finance

- Is Chaos theory in finance dead? (nice discussion on Willmott forum)

- The Misbehavior of Markets (book by Mandelbrot)

- Fractal Market Analysis: Applying Chaos Theory to Investment and Economics (book by Edgar Peter)

The book by mandelbrot intrigues me the most - I put it on my to read list out of curiosity

## Answer by vonjd (score 3, accepted)

https://quant.stackexchange.com/a/11473

I think one notable application of chaos theory (in the sense of non-linear dynamics) in financial markets is the work done by phyicist Didier Sornette.

You can find most of his publications and projects (actually lots of them) here on his page at the ETH Zürich: http://www.er.ethz.ch/fco

## Answer by Richi Wa (score 4)

https://quant.stackexchange.com/a/11472

Benoit Mandelbrot applied fractals and self-similarity to financial markets and the hurst exponent has its roots in chaos theory.

Look at this article from Wilmott magazine.

Just a personal note: I have not worked that much with this kind of theory so far but I also have not seen any of my peers being exceptionally sucessfull with these methods.

## Answer by George Han (score 0)

https://quant.stackexchange.com/a/53711

In short, yes, there are successful applications of chaos theory in quant finance.

I hope people find my answer helpful as I've done my master thesis on this topic. You can google Nassim Taleb and Mandelbrot together if you are not already familiar with Taleb and learn more about this.

Taleb adopted Mandelbrot's fractal hypothesis as an asset return model and concluded that our textbook way of measuring risk in financial markets as calculating standard deviations is insufficient and sometimes incorrect. If you believe financial markets is following the fractal model, then you cannot exclude events with infinite variance which means tail risks are always underestimated. The market is therefore inefficient and there's asymmetrical opportunities waiting to be taken advantage of. A hedge fund Empirica Capital LLC, founded by Taleb, had a return of 3600% in 1 month in 2020, following this strategy. I guess this counts as one of 'Successful applications of Chaos Theory in Quant Finance'.

## Answer by Hamish Gibson (score 0)

https://quant.stackexchange.com/a/53712

Whilst this doesn't apply to chaos theory, it does apply in regards to using theories outside the realm of Computer Science and Economics. In research it appears that 'Econophysics' is being more widely studied. You are correct that most research is just a broad statement about how theory X could apply to reality Y followed by not much marginal gain in insight, but every now and then this leads to a groudbreaking new theory. Don't forget, some of the theory behind Options pricing and the Black-Scholes model was borrowed from physics and brownian motion!

See : https://books.google.com/books?hl=en&lr=&id=XcZwuHGRxsgC&oi=fnd&pg=PR7&dq=louis+bachelier&ots=6jBYF0awNS&sig=nhwXrgohgpXmxAJ2wKpynsIPg-M about Louis Bacheliers work.

Additionally, the paper here http://www.sciencedirect.com/science/article/pii/S0960077918310233 investigated chaotic properties of Bitcoin prices when in a Deep learning network and yielded impressive results.