Perturbative Solution of the SABR Eikonal Equation

5 Pages Posted: 9 Jun 2017

Date Written: June 8, 2017


Abstract In this paper we give a new derivation of the leading order term of the implied volatility in the SABR model. As is widely know, Hagan et al. obtained an analytic formula for the implied volatility via asymptotic expansion. It has been argued that the leading order term of this expansion contains an error and some authors have recalculated it using different methods. Here we give another derivation using standard perturbation theory of the underlying eikonal equation. Our result agrees with that found by Berestycki et al.

Keywords: SABR model, implied volatility, eikonal equation, perturbation theory, Z-transform

JEL Classification: C02

Suggested Citation

Vanyolos, Andras, Perturbative Solution of the SABR Eikonal Equation (June 8, 2017). Available at SSRN: or

Andras Vanyolos (Contact Author)

Independent ( email )

No Address Available

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