A General Asymptotic Implied Volatility for Stochastic Volatility Models
| dc.creator | Henry-Labordere, Pierre | |
| dc.date | 2005-04-13 | |
| dc.date | 2005-05-13 | |
| dc.date.accessioned | 2026-07-07T03:04:43Z | |
| dc.date.available | 2026-07-07T03:04:43Z | |
| dc.description | In this paper, we derive a general asymptotic implied volatility at the first-order for any stochastic volatility model using the heat kernel expansion on a Riemann manifold endowed with an Abelian connection. This formula is particularly useful for the calibration procedure. As an application, we obtain an asymptotic smile for a SABR model with a mean-reversion term, called lambda-SABR, corresponding in our geometric framework to the Poincaré hyperbolic plane. When the lambda-SABR model degenerates into the SABR-model, we show that our asymptotic implied volatility is a better approximation than the classical Hagan-al expression . Furthermore, in order to show the strength of this geometric framework, we give an exact solution of the SABR model with beta=0 or 1. In a next paper, we will show how our method can be applied in other contexts such as the derivation of an asymptotic implied volatility for a Libor market model with a stochastic volatility. | |
| dc.description | 35 pp. References added. Some typos corrected | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0504317 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0504317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/26190 | |
| dc.subject | Other Condensed Matter | |
| dc.title | A General Asymptotic Implied Volatility for Stochastic Volatility Models | |
| dc.type | text |