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SOFR Transition Changes the Caplet Count in a One-Year Cap

Article Quant Q&A · Author: Sebastian
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Summary

The note explains how the transition from LIBOR to SOFR affects the optionlets included in a standard one-year USD interest-rate cap. In the LIBOR convention described, the first rate fixing is already known at the start date, so the cap begins with the later caplets and excludes the initial period. Under the SOFR convention discussed, the compounded rate for that first period is not known until the period ends.

As a result, the first optionlet is included in the cap’s price, giving the one-year cap four caplets rather than three in the stated example. The answer is direct and provides no derivation, market convention details, or broader comparison of cap specifications. The count should therefore be understood in the context of the conventions described in the question, rather than as a universal rule for every product labeled a one-year cap.

Key ideas

  • Under the LIBOR convention described, the initial period’s rate is known at the start and its caplet is excluded.
  • For the SOFR convention discussed, the first compounded rate is determined only after its accrual period.
  • Including that first optionlet makes the example one-year USD cap consist of four caplets.
  • The stated count depends on the cap conventions described in the note.

Tags

Fixed incomeOptionsDerivatives pricing
Full text
# How many caplets has a 1Y USD Cap after Libor transition?


# How many caplets has a 1Y USD Cap after Libor transition?












A standard 1Y USD Cap in the Libor world had 3 caplets, the first one starting in 3 months from today. There was no caplet from t=0 to t=0.25 because the first rate was already known at time 0. Now, in the SOFR world, the rate for the first caplet is not known until time 0.25, so I guess it is included in the price of the standard caps that are quoted. Does this mean that the 1Y cap has now 4 caplets instead of 3?

## Answer by KevinT (score 4, accepted)

https://quant.stackexchange.com/a/81820

Yes, your understanding is correct, the first optionlet can no longer be excluded, since the fixing of the compound rate will only occur after 3 months. Hence, the 1y cap would now be comprised of four caplets.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.