Implied Volatilities for Options on Backward-Looking Term Rates

18 Pages Posted: 12 Jun 2020

See all articles by Karl F. Hofmann

Karl F. Hofmann

Deloitte GmbH Wirtschaftsprüfungsgesellschaft

Date Written: May 5, 2020


We derive valuation formulas for caps and floors on backward-looking term rates in the Black-1976, Bachelier and Hull-White-1-Factor models explicitly regarding valuation in the fixing period, extending and detailing results of [Lyashenko & Mercurio 2019, Henrard 2019, Turfus 2020]. These formulae facilitate us to provide a consistent definition for implied volatility on backward-looking term rates.

Keywords: IBOR Replacement, RFR, SOFR, Market Model, Forward Rates, Hull-White Model

JEL Classification: C22, C60, G12, G13

Suggested Citation

Hofmann, Karl Friedrich, Implied Volatilities for Options on Backward-Looking Term Rates (May 5, 2020). Available at SSRN: or

Karl Friedrich Hofmann (Contact Author)

Deloitte GmbH Wirtschaftsprüfungsgesellschaft ( email )

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