Analytic Short Rate Model with Smile and Skew

23 Pages Posted: 6 May 2021 Last revised: 28 Dec 2022

See all articles by Colin Turfus

Colin Turfus

Deutsche Bank

Aurelio Romero-Bermudez

ABN AMRO - ABN-Amro Bank, The Netherlands; Deutsche Bank

Date Written: May 5, 2021


We consider an extension of the Hull-White short rate model which incorporates smile and skew, effectively through a quadratic dependence of the diffusion on the short rate. We derive an asymptotic representation of the pricing kernel for this new model in semi-analytic form, using this to obtain accurate, easily computed, asymptotic formulae for zero coupon bonds and LIBOR options. Unlike comparable models such as SABR, ours appears to be usable even for pricing options with long times to maturity. Further, the same calibrated model can be used for all possible maturities and LIBOR tenors.

Keywords: short rate model, skew, smile, analytic solution, perturbations methods, asymptotic, caplet, swaption

JEL Classification: G13

Suggested Citation

Turfus, Colin and Romero-Bermudez, Aurelio, Analytic Short Rate Model with Smile and Skew (May 5, 2021). Available at SSRN: or

Colin Turfus (Contact Author)

Deutsche Bank ( email )

Winchester House
1 Great Winchester Street
London, EC2N 2DB
United Kingdom

Aurelio Romero-Bermudez

ABN AMRO - ABN-Amro Bank, The Netherlands ( email )

NL-1000 EA Amsterdam

Deutsche Bank ( email )

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