8th Annual Symposium
Physics of Cancer
Leipzig, Germany
October 4-6, 2017
Contributed Talk
An intriguing similarity between cancer metastasis and financial markets
Christoph Mark, Claus Metzner, Lena Lautscham, Ben Fabry
Friedrich-Alexander University Erlangen-Nürnberg, Department of Physics, Biophysics group, Henkestraße 91, Erlangen, Germany
Contact:  | Website
Invasive cancer cells and exchange-traded stocks (or funds) share a common feature: they are complex systems. In cancer metastasis, the apparently random motions of migratory cancer cells are the result of a vast network of underlying intra-cellular processes that act on different time-scales and drive cell migration. Furthermore, the cell may interact with a highly heterogeneous extra-cellular matrix. In the same way, the price fluctuations of a financial asset are the result of a multitude of transactions, carried out on time-scales that differ in several orders of magnitudes. While traditional investors may hold positions for several years, day traders carry out multiple transactions per day, and high-frequency hedge funds even trade in the milli- and microsecond regime. As a result of these broad ranges of underlying driving processes, the observable data (cancer cell movements and price fluctuations) do not follow conventional statistics. Both the step width distribution of migratory cells and the distribution of stock log-returns resemble a two-sided exponential distribution (also called Laplace distribution), instead of the ubiquitous Bell-shaped normal distribution. In other terms, extreme fluctuations, whether in cancer cell movements or stock price variations, are significantly underrepresented by conventional models that rely on the normal distribution. In fact, the use of the normal distribution in financial risk assessment is suspected to have played a significant role in recent financial crises.

Here, we present a novel method to rescue the use of simple, well-known statistical models like the normal distribution to describe the dynamics of complex systems, by proposing a hierarchy of two models. On short time scales, we have found that the movements of cancer cells as well as the stock price fluctuations still adhere to the normal distribution. On longer time scales however, the parameters of this normal distribution (i.e. the mean value and the variance) themselves show significant stochastic variations. By combining a low-level Gaussian model with a high-level model that describes how the low-level parameters change over time, we can provide a better fit to the observed data, compared to a model with static parameters. The “anomalous” two-sided exponential distribution then arises naturally from the superposition of normal distributions with varying variances. Furthermore, this two-level approach is able to uncover essential details about the dynamics of complex systems that would have been averaged out by the use of static parameters.

Comparing the migration dynamics of four different cell types on a 2-dimensional substrate, we find that cells that exhibit phases of simultaneously high directional persistence and migration speed are also more invasive in 3-dimensional collagen gels. These efficient phases of both high persistence and speed also exist in the price dynamics of stock markets. Comparing the daily close prices from 2010 to 2016 of all stocks in the NASDAQ-100 index, we find that stocks that exhibit phases of simultaneously high volatility (analogous to cell speed) and momentum (analogous to directional persistence) perform better, compared to stocks for which volatility and momentum are non-correlated or negatively correlated.

The work not only provides new insights into both cancer cell migration and trading dynamics, but further illustrates the importance of reaching out to different fields of research (even all the way down to finance) in the effort to unravel the underlying principles that govern complex systems.
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