Asymptotic Implied Volatility at the Second Order with Application to the SABR Model

By L. Paulot. 2009

88 citations recorded by the source corpus.

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.

Subfields: Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/5574bad061d0f3dceb5498834a85ad422fce6457

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Martin Forde
2. Antoine Jacquier
3. Peter K. Friz
4. Ismaël F. Bailleul

In Finance

1. Antoine Jacquier
2. Peter K. Friz
3. S. Violante
4. Martin Forde
5. Jean-Dominique Deuschel
6. Nicolas Victoir
7. T. Cass
8. Martin Hairer

Citations in the corpus

• Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “Such expansions have also been discussed, based on heat kernel expansions on Riemannian manifolds by [16, 32, 45], not always in full mathematical rigor.”
• SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL (2009, methodology): “[21], Henry-Labordère [22] and Paulot [35]).”