Outside the domain of Wall Street, the parallels between physical concepts and finance are sometimes taken more literally by academics. Kirill Ilinski of the University of Birmingham in England has used Feynman’s theory of quantum electrodynamics to model market dynamics, while employing these concepts to rederive the Black-Scholes equation. Ilinski replaces an electromagnetic field, which controls the interaction of charged particles, with a so-called arbitrage field that can describe changes in option and stock prices. (Trading that brings the value of the stock and the option portfolio into line is called arbitrage.)
Ilinski’s theory shows how quantum electrodynamics can model Black, Scholes and Merton’s hedging strategy, in which market dynamics dictate that any gain in a stock will be offset by the decline in value of the option, thereby yielding a risk-free return. Ilinski equates it with the absorption of “virtual particles,” or photons, that damp the interacting forces between two electrons. He goes on to show how his arbitrage field model elucidates opportunities for profit that were not envisaged by the original Black-Scholes equation.
Ilinski is a member of the nascent field of econophysics, which held its first conference last July in Budapest. Nevertheless, literal parallelism between physics and finance has gained few adherents. “It doesn’t meet the very simple rule of demarcation between science and hogwash,” notes Nassim Taleb, a veteran derivatives trader and a senior adviser to Paribas, the French investment bank. Ilinski recognizes the controversial nature of his labors. “Some people accept my work, and some people say I’m mad. So there’s a discrepancy of opinion,” he says wryly.
Whether invoking Richard Feynman or Fischer Black, the use of mathematical models to value and hedge securities is an exercise in estimation. The term “model risk” describes how different models can produce widely varying prices for a derivative and how these prices create large losses when they differ from the ones at which a financial instrument can be bought or sold in the market.
Model risk comes in many forms. A model’s complexity can lead to erroneous valuations for derivatives. So can inaccurate assumptions underlying the model—failing to take into account the volatility of interest rates during an exchange- rate crisis, for instance. Many models do not cope well with sudden alterations in the relation among market variables, such as a change in the normal trading range between the U.S. dollar and the Indonesian rupiah. “The model or the way you’re using it just doesn’t capture what’s going on anymore,” says Tanya Styblo Beder, a principal in Capital Market Risk Advisors, a New York City firm that evaluates the integrity of models. “Things change. It’s as if you’re driving down a very steep mountain road, and you thought you were gliding on a bicycle, and you find you’re in a tractor-trailer with no brakes.”
Custom-tailored products of financial engineering are not traded on public exchanges and so rely on valuations produced by models, sometimes making it difficult to compare the models’ pricing to other instruments in the marketplace. When it comes time to sell, the market may offer a price that differs significantly from a model’s estimate. In some cases, a trader might capitalize on supposed mispricings in another trader’s model to sell an overvalued option, a practice known as model arbitrage.
“There’s a danger of accepting models without carefully questioning them,” says Joseph A. Langsam, a former mathematician who develops and tests models for fixed-income securities at Morgan Stanley. Morgan Stanley and other firms adopt various means of testing, such as determining how well their models value derivatives for which there is a known price.