29 Sep 2010, Laurie Carver, Risk magazine
The flash crash in May this year was marked by persistent kurtosis levels, in contrast to most market panics where the measure drops, and can be modelled using the physics of spontaneous self-organization, says a top quant.
Lisa Borland, head of derivatives strategies at San Francisco-based hedge fund Evnine & Associates, has designed a model inspired by the physics of supercool magnets that captures this statistical signature.
"I was thinking of a panic as a kind of regime change, and it reminded me of spontaneous symmetry breaking in physics, when a system will undergo a phase transition and change many of its fundamental properties," she says.
In the model, stocks are likened to the particles in a magnet, and their upward or downward trend analogous to an intrinsic variable known as spin. At normal temperatures, these spins are distributed randomly within the magnet, but near absolute zero they align. In the analogy, the role of temperature is played by the inverse of volatility, so in a period of turmoil the stocks all move in the same direction, and hence exhibit strong correlation.
The key to the flash crash comes in the way the magnet is cooled – a uniform temperature decrease will yield a Gaussian return distribution, while concentrating the cooling effect will produce greater kurtosis. This corresponds to uniform and local volatility shocks respectively – with the latter case ideal for describing the flash crash's origin in one sudden batch of sell orders by high-frequency traders.
A US Securities and Exchange Commission inquiry is due to report its findings on the flash crash by the end of September.
A more in-depth article on the model will appear in the October issue of Risk.
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