The Cusp Catastrophe Fold Line is a moment in both price and time where participants in complex domains (like trading markets) realize that there has been a sudden regime change.

The Cusp Catastrophe Model is one of those 'explain everything' models that help make behavioral sense of so many things including:

  • Stock Market Crashes

  • Volatility Crashes

  • Housing Market Crashes

  • Choice Behavior in retail E-commerce

  • Industrial Innovation

  • Online Art Auctions

  • Human concern for Global Warming

Baruník, Jozef, and M. Vosvrda. "Can a stochastic cusp catastrophe model explain stock market crashes?." Journal of Economic Dynamics and Control 33, no. 10 (2009): 1824-1836.

Barunik, Jozef, and Jiri Kukacka. "Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility." Quantitative Finance 15, no. 6 (2015): 959-973.

Diks, Cees, and Juanxi Wang. "Can a Stochastic Cusp Catastrophe Model Explain Housing Market Crashes?." Journal of Economic Dynamics and Control 69 (2016): 68-88.

Huang, Yu Kai, and Cheng-Min Feng. "An analysis on choice behavior on the pick-up point for the e-commerce retailing delivery using a cusp catastrophe model." In Proceedings of the Eastern Asia Society for Transportation Studies Vol. 6 (The 7th International Conference of Eastern Asia Society for Transportation Studies, 2007), pp. 133-133. Eastern Asia Society for Transportation Studies, 2007.

Herbig, Paul A. "A cusp catastrophe model of the adoption of an industrial innovation." Journal of Product Innovation Management 8, no. 2 (1991): 127-137.

Xiang, Yong, Yu-Kai Huang, Shih-Wei Hsu, and Kwok-Leung Li. "A cusp catastrophe model for developing marketing strategies for online art auction." " International Journal of Electronic Commerce Studies" 4, no. 1 (2014): 111-120.

Mostafa, Mohamed M. "World-wide concern for global warming: a stochastic cusp catastrophe analysis." International Journal of Green Economics 13, no. 1 (2019): 19-39.

Where Did This Come From?

French mathematician Rene Thom in the 1960s:

Cusp Catastrophe Theory is a special branch of dynamical systems theory studying and classifying phenomena characterized by sudden shifts in behavior that arise from small change in circumstance.

The idea of the Cusp Catastrophe Fold Line helps us understand things like why a ship might suddenly tip over at sea or why a bridge might suddenly collapse.

"If AAPL’s price crosses below the Fold Line, then market participants will suddenly realize they are in a new regime altogether."

It’s Like The Road Runner

The Fold Line is like the cliff that Wile E. Coyote runs off, but before he has looked down…suddenly realizing he’s in a new regime altogether.

By framing key price and time parameters a certain way, The Fold Line Report identifies scenarios where small changes in price can lead to sudden, dramatic shifts in that market’s perception of that price.

Markets tend to fluctuate near this bifurcation point, simultaneously drawn by forces of both attraction and repulsion — in equilibrium — yet susceptible to collapse.

The Fold Line Report offers the precise coordinates of metastable precipices — well in advance — yielding almost unbelievable market-timing precision.

The Fold Line Report alerts when a price nears its own Cusp Catastrophe Fold Line — a level others likely don’t see at all — illuminating the gradients driving markets toward (and then suddenly away from) fleeting stability.