Article by: Laurie Carver
Published by: Risk Magazine
Date: 4 May 2012
“There has been a long history of interaction between physics and quantitative finance. Now a technique for finding the effects of small fluctuations in quantum fields is being used to get a handle on the implied volatility smiles a stochastic model can create. Laurie Carver introduces this month’s technical articles.
“In Stochastic volatility’s orderly smiles (see pages 60–66), Lorenzo Bergomi, head of quantitative research, global markets at Société Générale Corporate & Investment Banking (SG CIB) in Paris, and Julien Guyon, a senior analyst in his team, use a quantum mechanical technique known as perturbation theory to determine the possible volatility smiles a stochastic volatility model can produce.
Exact equations are given for the form of the at-the-money implied volatility, the skew and the curvature.”
Full article (Subscription required): Link