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Mapping Caplet Expiry and Tenor to a LIBOR Forward Rate

Article Quant Q&A · Author: Yassine Q.
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Summary

This exchange clarifies which forward LIBOR rate corresponds to a caplet’s expiry and accrual tenor in a multi-curve LIBOR Market Model. The example uses a caplet expiring in three years with a half-year tenor. Its underlying rate is the forward rate for the period beginning two and a half years from today and ending at the three-year point.

The explanation follows directly from the dates: a caplet’s tenor is the length of its accrual period, and its expiry is the end of that period in the example’s convention. This helps identify the rate input for the analytical pricing formula. The answer addresses date mapping only; it does not derive the pricing formula, discuss multi-curve basis dynamics, or validate an implementation against numerical results.

Key ideas

  • A caplet’s tenor specifies the length of its underlying accrual period.
  • For a three-year expiry and a half-year tenor, the relevant forward period runs from 2.5 to 3 years.
  • The forward LIBOR rate for that period is the rate used as the caplet’s underlying rate in the stated example.
  • Correct date mapping does not by itself establish that a multi-curve pricing implementation is correct.

Tags

Fixed incomeDerivatives pricingOptionsStatistics
Full text
# Libor Market Model Implementation


# Libor Market Model Implementation












I'm trying to implement an LMM-MultiCurve for caplet pricing following the analytical formula mentioned in this article (pg 20):

https://www.researchgate.net/publication/326012245_LIBOR_market_model_with_multiplicative_basis

However, I didn't get the same results. I think my error comes from the lack of understanding regarding the evolution of LIBOR rate and its tenor structure.

Could anyone give me some insight about it ?

For example a Caplet with Expiry of 3year with tenor = 0.5 has to be priced (following the analytical formula) with the LIBOR rate L(0,2.5,3). Am I getting it right ?

Many thanks for your help.

## Answer by TomDecimus (score 1)

https://quant.stackexchange.com/a/42948

For example a Caplet with Expiry of 3year with tenor = 0.5 has to be priced (following the analytical formula) with the LIBOR rate L(0,2.5,3). Am I getting it right ?

Thats right. The caplet hast a tenor of half a year and expires in 3 more years, therefore it starts at T =2.5 and ends at T = 3. (Which in this case is the forward rate)

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