Stock patterns

Mathematician Niteesh Sahni one day stumbled upon a 2017 research paper that had used an unusual kind of geometry to analyse images of human brains and extract patterns linked to Parkinson's disease. After spending a decade immersed in abstract mathematics, Sahni, a faculty member at the Shiv Nadar University (SNU), Noida, had turned his gaze towards applied mathematics.

The paper (bit.ly/hyperbolic-geometry) gripped Sahni's attention. It described research led by Carlo Cannistraci, an Italian scientist exploring "the physics and engineering of complexity and intelligence". Cannistraci and his colleagues had used hyperbolic geometry – a curved space where parallel lines can diverge, and the angles in a triangle can add to less than 180 degrees – to study the brain. The geometry helped uncover hidden patterns in the dense and intricate connectivity between brain regions to distinguish between brains with Parkinson's disease and healthy ones. Inspired by the paper, Sahni wondered: Could hyperbolic geometry be used to probe the stock market?

"Imagining the stock market as something like the brain appears outrageous," says Sahni, Associate Professor of Mathematics at SNU. "But there are some similarities." With roughly 86 billion neurons and trillions of synapses or interconnections between them, the human brain is among the most intricate complex systems known.

The stock market is far less complex. But, Sahni reasoned, the market also displays emergent behaviour: larger responses arising from the interaction of individual parts without any single part directing the outcome. Price movements emerge from millions of individual buy-or-sell actions. Both brains and stock markets are noisy and dynamic, with ever-changing internal structures that respond to external stimuli. In the brain, connected regions often become active at the same time; similarly, in markets, correlated stocks often tend to rise and fall in sync. It seemed possible to view stocks as nodes, or brain regions, and their correlations as the links connecting them.