D. Modeling Financial Turbulence

Quantum Chaos Applications to Financial Turbulence Modeling

Discussion on the article:

“Financial Turbulence, Business Cycles and Intrinsic Time in an Artificial Economy”, Gonçalves, C.P., Algorithmic Finance (2012), 1:2, 141-156, (quoted in the text below as Gonçalves (2012)).

http://algorithmicfinance.org/1-2/pp141-156/

The latest sub-prime crisis presented the financial practitioners’ community as well as the science community with evidence regarding financial risk, synthesized in the expression “too big to fail”, the “too big to fail” expression entails a recognition of a systemic interdependence that characterizes global financial risk interconnectivity: the interconnected financial web is such that there are nexa (too big to fail nodes) whose collapse can lead to a global crisis, or even to a global systemic collapse.

Individual corporations, even if they do not have any of their funds invested in high risk assets are exposed to the risk of the financial nexa.

On the other hand, in the financial system, prices have been put on risk, packageable to be manageable and resold, hedged and speculated upon, transferred through derivatives, assets whose payoff profile is contingent upon some underlying asset performance so that they can be used both for hedging as well as for building elaborate bets upon the underlying asset’s performance.

Hedging itself takes place under a risk transfer procedure that allows the investor to cover the exposure by effectively selling it to some counter-party. One might think that, in this way, risk exposure is conserved, so that there is at least one speculator willing to hold the risk of a hedger, or an investment fund willing to invest on a risk exposure being sold in the market for financial risk.

However, risk is not conserved, by circulating the risk exposure, trading dynamics of financial agents worldwide is generating new linkages between portfolios, so that even if some of the portfolios do not have a direct exposure to high risk assets, they may still suffer contamination losses due to market falls linked to some well dispersed high risk assets (this took place with the subprime crisis), such contamination effect constitutes evidence of complex field dynamics.

The analysis of financial risk and, more generally, risk analysis needs to draw upon network field dynamics.

In the global financial and economic networks' coevolving dynamics, multiple fields interact leading to the observed patterns of price and returns series.

When one considers a system of companies with traded shares, several fields have observable dynamics from available data: shares’ price field; financial returns field; financial volatility field (calculated for an appropriate volatility measure).

In each of these fields, turbulence markers can be seen. Below is a picture of the main features of financial turbulence.

A Picture of Financial Turbulence

Turbulence is a permanent presence in the financial price dynamics, taking place at different scales and leading to tail risk observable in terms of excess kurtosis of the empirical returns' distributions, dynamical bursts related to clustering volatility and market activity (including transaction volume), nonlinear dependence and long memory in volatility, bubbles and crashes and sudden price jumps, as well as scaling turbulent phases.

Scaling turbulence means that, at different scales of observation, one can see markers of turbulence visually identifiable in immediate terms by dynamical bursts, clustering and long memory in the volatility dynamics, as well as sudden jumps with respect to the local “typical” fluctuations.

Scaling of Turbulence in the S&P 500 Index

The main hypothesis, within the complexity sciences, has been that such turbulent patterns emerge from the financial agents’ adaptive learning and trading schemata's coevolving dynamics. A hypothesis that has been addressed by agent-based computation applied to financial market modeling.

However, the financial coevolving dynamics is not restricted to its traders’ ecologies, indeed, the financial system coevolves with the economic system: financial systems interact with both local and globally operating companies, so that financial economy and real economy form part of an entangled web of business in which the flow of coin, cash, debt, information and knowledge are like the life blood of the system. Traders’ expectations and trading patterns have a systemic causality that goes beyond that of the financial system, it affects the economic dynamics.

Thus, a model of financial dynamics without the underlying business economic dynamics is incomplete, since the value-driver dynamics is either absent or tucked away to the form of a global noise term. On the other hand, a model of economic dynamics without the financial dynamics is also incomplete, since the financial system is not simply an evaluator it is also a source of business facts and dynamics. It is, therefore, necessary to model the coevolution between the real economy and the financial system.

Modeling the Coevolution between the Real Economy and the Financial System

In Gonçalves (2012), this problem is tackled within quantum econophysics, combining quantum chaos theory and quantum optimization to the integrated financial modeling of real economy and financial market coevolving dynamics, this is done within an integrated modeling approach that shows the emergence of turbulence and scaling patterns in the financial returns’ dynamics, resulting from the coevolution of competing companies in a market economy and a financial market comprised of value investors and arbitrageurs, thus establishing a bridge to evolutionary arbitrage theory.

The model generates turbulence both in the financial and economic systems, in such a way that, for some parameter range, turbulence is seen at the microscopic level (company level) as well as at the macroscopic level (market portfolio level), as can be seen below.

Financial Output from Simulation of the Quantum Artificial Economy for 100 Competing Companies

Methodologically, what does this all mean for the social sciences in general?

One might be led to think that applications of quantum theory to social sciences would be a return of “social physics” in the quantum version now, but this is not exactly the case. While quantum econophysics is, indeed, physics applied to economics, it also has paradigmatic consequences that go beyond a “just social physics” label, since one is addressing, mathematically, social systems as complex systems with an evolutionary computing dynamics that is formally equivalent to evolutionary quantum computation. Econophysics is, indeed, physics and economics mathematically synergized to address complex economic dynamics.

Notions of fields, chaos and quantized state variables are characteristic of different complex systems and are generalizable as effective in addressing complex systems and interconnected risk field dynamics, which explains both the need for a combined research program of quantum complex systems science and quantum risk science.

The quantum model proposed in (Gonçalves, 2012) is already a step in that direction.