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LIBOR Market Model Tenors Are Fixed Calendar Dates

Article Quant Q&A · Author: user357269
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Summary

The document clarifies what the tenor dates represent in the LIBOR market model. The modeled quantities are forward rates over intervals bounded by fixing and maturity dates. These are calendar dates, so the dates remain fixed as time advances; they do not shift forward simply because the model is recalibrated later.

The answers add a market-convention caveat: actual LIBOR accrual periods can reflect business-day adjustments, holiday calendars, modified following rules, and month-end consistency. Examples for GBP six-month LIBOR illustrate how a nominal six-month period may end on an adjusted business day, including cases where month-end treatment changes the date. The discussion explains the distinction between fixed contractual dates and tenor durations, but does not provide model equations or a full calibration procedure.

Key ideas

  • LIBOR market models represent forward rates over intervals bounded by fixing and maturity dates.
  • Those dates are calendar dates and do not roll forward when the model is recalibrated later.
  • Actual period dates can be adjusted using currency-specific business-day conventions.
  • Modified following and month-end consistency rules can affect the end date of a nominal tenor.

Tags

Fixed incomeDerivatives pricing
Full text
# LIBOR Market Model - tenors?


# LIBOR Market Model - tenors?












In the LIBOR market model, we have a bunch of forward rates $L_j$ on $[T_j, T_{j+1}]$ for some collection on $j$.

My question is, is it the delivery dates or the time to maturities that are fixed? So if I calibrate my model tomorrow, will it have the same underlyings as it did today, or will $L_j$ be $[T_j + \delta t, T_{j+1} + \delta t]$?

## Answer by Jiem (score 1, accepted)

https://quant.stackexchange.com/a/43447

In the libor market Model, what are modeled are the forward rates. Hence you have to see the fixing date $T_j$ and the maturity date $T_{j+1}$ as dates and not durations. Both are fixed dates and are the same at $t+\delta t$

## Answer by Attack68 (score 2)

https://quant.stackexchange.com/a/43436

Just to be precisely clear, your mathematical formulation will not necessarily capture the nuances of the physical dates that libor is valued between, due to holiday calendars and modification rules.

Take GBP for example. The LIBOR in that currency is subject to a Modified Following rule as well as a Month End Consistency rule.

For example: Generally 6M Libor starting on any date of the month will roll to the same date of the month 6 months ahead and be modified forwards if it is not a business day. But if this takes it to a new month it is modified backwards. And, in GBP, if it starts on month end it ends on month end:

6M starting Wed Feb 27th 2019 ends on Tues 27th Aug 2019 (no adj. needed) 6M starting Thu Feb 28th 2019 ends on Fri 30th Aug 2019 (month end modified) 6M starting Wed May 29th 2019 ends on Fri 29th Nov 2019 (no adj. needed) 6M starting Thu May 30th 2019 ends on Fri 29th Nov 2019 (modified following) 6M starting Fri May 31st 2019 ends on Fri 29th Nov 2019 (modified following) 6M starting Thu May 16th 2019 ends on Mon 18th Nov 2019 (following)

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