Volatility Library

Article by: Julien Guyon and Pierre Henry-Labordère
Published by: risk.net/risk-magazine
Date: Jan 2012

“Following previous work on the calibration of multifactor local stochastic volatility models to market smiles, Julien Guyon and Pierre Henry-Labordère show how to calibrate exactly any such model. Their approach, based on McKean’s particle method, extends to hybrid models, where interest rates are also stochastic. They illustrate the efficiency of their algorithm on hybrid local stochastic volatility models.”

Full article (PDF): Link

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

Article by: Jared DeLisle, James S. Doran, Kevin Krieger
Published by: Department of Finance, Florida State University
Date: 3 Mar 2010

“The ability to hedge market downturns without sacrificing upside returns has long been sought by all investors. We consider alternative methods of hedging the S&P 500 with assets that mimic the VIX index in hopes of taking advantage of the asymmetric relationship between volatility and returns. We first demonstrate that if the VIX was investable, and using the fact that volatility mean-reverts, can results in significantly improved portfolio performance over the buy-and-hold index portfolio. However, using VIX futures in a similar fashion does not provide the same results. As such, we deconstruct the VIX Index to find the relevant S&P 500 options that drive the VIX movements. In doing so, we then form a synthetic VIX portfolio using the S&P 500 options and capture returns similar to the VIX index. Our synthetic portfolio is highly liquid and investable, and when combined with a long position in the S&P 500, generates significantly higher returns with lower risk than the buy-and-hold S&P 500 index portfolio.”

Full article (PDF): Link