On New Year’s Day 1995, a single giant wave hit the Draupner oil
platform in the North Sea off the coast of Norway. By chance, the
platform was fitted with laser measuring equipment which recorded the
height of waves as they passed by. This one measured in at an unprecedented 25.6
metres, about the size of a seven storey office block. The Draupner
event finally confirmed the existence of rogue waves, previously
known only to science through the anecdotal evidence of the few who
had seen and survived them.
Curiously, the existence of rogue waves was predicted
mathematically more than ten years earlier by Howell Peregrine at the
University of Bristol in the UK. The theoretical prediction and the
observational confirmation should have generated an obvious question:
shouldn’t rogue waves also occur in other wave-like systems?
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And yet it wasn’t until 2007 that the first optical rogue waves
were observed in an optical fibre. Since then things have moved
rapidly. This blog recently discussed the
first measurement of rogue microwaves and earlier this year
another group predicted the existence of rogue matter waves using
numerical simulations.
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But what of more abstract systems? Today 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.
That’s interesting. There’s no shortage of anecdotal evidence for the
existence of financial rogue waves. Look at the Asian financial
crisis of 1997 or the current global financial crisis. But
econophysicists will want more than that to confirm that financial rogue
waves really exist.
Perhaps what they need now is the financial equivalent of the Draupner oil
platform measuring ambient wave height and waiting for the big one to
hit.
