Suppose that today the price of a 3m LIBOR caplet with 6m expiry has been calibrated with a particular implied volatility.

How would one go about thinking about an adjustment to that volatility to account for the price of a caplet which is not based on 3m LIBOR but on 3m compounded OIS/SOFR. There seems to be a number of practical issues:

• the OIS caplet must have an expiry 3m greater than that of the LIBOR caplet to account for all possible interim fixings.
• the OIS caplet's volatility will be affected by the volatility of each contributing OIS rate within the 3m period.
• the OIS and LIBOR may have a basis so that strike may be further/nearer the underlying expected rate.

The adjustment is required since we have existing LIBOR framework and systems which will temporarily adopt OIS caplets (proxied by LIBOR) with that adjustment to get closer to true value.

Estimated or more specific quantitatively theoretic answers all appreciated.

Suppose that today the price of a 3m LIBOR caplet with 6m expiry has been calibrated with a particular implied volatility.

How would one go about thinking about an adjustment to that volatility to account for the price of a caplet which is not based on 3m LIBOR but on 3m compounded OIS/SOFR. There seems to be a number of practical issues:

• the OIS caplet must have an expiry 3m greater than that of the LIBOR caplet to account for all possible interim fixings that are compounded over the period.
• the OIS caplet's volatility will be affected by the volatility of each contributing OIS rate within the 3m period, which occur on different dates.
• the OIS and LIBOR may have a basis so that strike may be further/nearer the underlying expected rate.

The adjustment is required since we have existing LIBOR framework and systems which will temporarily adopt OIS caplets (proxied by LIBOR) with that adjustment to get closer to true value.

Estimated or more specific quantitatively theoretic answers all appreciated.