New simple model predicts financial market, complete with crashes

27 January 2012

Photo by theboybg/ Flickr

The failure of financial models to allow for extreme market behaviour is considered to have significantly exacerbated the impact of the 2008 financial crisis. Now, a simple modification to existing equations, suggested by researchers at UCL, has produced predictions of evolving share prices much more in line with market reality.

Improved financial models are key to understanding how to stabilize an economy. Professor William Shaw (UCL Computer Science and Maths) and UCL PhD candidate Marcus Schofield argue that including a simple model of price feedback is all that’s needed to explain several market phenomena.

Writing in the online issue of the journal Quantitative Finance, they suggest that this price feedback element comes from technical trading – where investors base their decisions on the history and analysis of stock performance. This is a complex phenomenon, with psychology and mood as well as bare facts playing a part.

This complexity means that large computer simulations are needed to replicate the effects of technical traders – but the work of Shaw and Schofield seems to indicate that a great deal of insight and realistic behaviour can be obtained from a simple mathematical representation developed in the paper.

In the paper, “A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback”, Shaw and Schofield submit a possible answer found by blending together the probabilistic processes traditionally used for this sort of modelling. Such hybrids predict extreme movements much more frequently than they are expected to be in traditional models associated with the Gaussian distribution.

Graphing the changing prices illustrates that the scale of price movements so far impact the scale of subsequent moves

Professor Shaw said: “Recent events have certainly shown us that extreme movements do happen – even ‘several days in a row’, as the CFO of Goldman Sachs commented. These blended models can also produce sudden bubbles and crashes easily, just as (unfortunately) in the real world.”

Professor Shaw added: “This is a surprisingly simple way of thinking about problems that have troubled financial mathematicians for ages, and I hope it will be useful in understanding the sort of freak market behaviour that can have such dramatic consequences.”

Above photo by theboybg on Flickr, made available through a Creative Commons licence
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