For Libor we have the following Convexity adjustment formula for payment delay (under normal model)

$$CA = P(0,T_e,T_p)\rho\sigma_e^L\sigma_p^L\Delta_e^p(T_s-t_0)$$


  1. $T_s$ is the period start date

  2. $T_e$ is the period end date

  3. $T_p$ is the payment date (assuming here $T_p$ > $T_e$)

  4. $P(0,T_e,T_P)$ is discount factor from $T_e$ to $T_p$

  5. $rho$ is correlation between 2 forward rates $F(t_0,T_s,T_e)$ and $F(t_0,T_e,T_p)$

  6. $\sigma_e^L$ is vol of $F(t_0,T_s,T_e)$

  7. $\sigma_p^L$ is vol of $F(t_0,T_e,T_p)$

How would this formula change for RFR compounded (SOFR) rates? A naïve way would be to just replace the Libor vols with backward looking RFR vols and change the $T_s$ to $T_e$ something like this

$$CA = P(0,T_e,T_p)\rho\sigma_e^{RFR}\sigma_p^{RFR}\Delta_e^p(T_e-t_0)$$

wondering is somebody did a proper derivation for daily compounded rates like SOFR.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.