The Physics arXiv Blog reports on a paper that suggests that if financial markets behave like nonlinear wave-like systems, then rogue waves are an inevitable consequence.
...Zhenya Yan at the Institute of Systems Science in Beijing says that rogue waves can also occur in financial systems, and in particular in equity markets. Traditionally, econophysicists have modelled equity pricing using the Black-Scholes economic model, in which prices change stochastically, like the movement of particles under Brownian motion.
Researchers have long known that the Black-Scholes model cannot account for the observed volatility of the real market but had no alternative to turn to. However, earlier this month, Vladimir Ivancevic at the Defence Science & Technology Organisation in Australia proposed a nonlinear wave model as an alternative to Black-Scholes.
The Ivancevic Option Pricing Model approximates to Black Scholes under certain circumstances but also allows for a rich variety of other behaviours and so has the potential to better describe real markets. Much of this behaviour is as yet unexplored.
Enter Yan, who points out today that one solution of a nonlinear wave system is a rogue wave, an event of far greater magnitude than would be expected by any standard method of analysis...
Financial Rogue Waves
Zhenya Yan
Abstract
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
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