Unifying the BGM and SABR Models: A short Ride in Hyperbolic Geometry
| dc.creator | Henry-Labordere, Pierre | |
| dc.date | 2006-02-15 | |
| dc.date.accessioned | 2026-07-07T12:11:27Z | |
| dc.date.available | 2026-07-07T12:11:27Z | |
| dc.description | In this short note, using our geometric method introduced in a previous paper \cite{phl} and initiated by \cite{ave}, we derive an asymptotic swaption implied volatility at the first-order for a general stochastic volatility Libor Market Model. This formula is useful to quickly calibrate a model to a full swaption matrix. We apply this formula to a specific model where the forward rates are assumed to follow a multi-dimensional CEV process correlated to a SABR process. For a caplet, this model degenerates to the classical SABR model and our asymptotic swaption implied volatility reduces naturally to the Hagan-al formula \cite{sab}. The geometry underlying this model is the hyperbolic manifold $\HH^{n+1}$ with $n$ the number of Libor forward rates. | |
| dc.identifier | https://arxiv.org/abs/physics/0602102 | |
| dc.identifier | http://arxiv.org/abs/physics/0602102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210222 | |
| dc.subject | Physics and Society | |
| dc.subject | Other Condensed Matter | |
| dc.subject | Computational Finance | |
| dc.title | Unifying the BGM and SABR Models: A short Ride in Hyperbolic Geometry | |
| dc.type | text |