Interpolating Missing LIBOR Tenors for Contractual Use
Summary
The discussion considers how to obtain a nine-month LIBOR fixing when that tenor is unavailable. It emphasizes that interpolation depends on the intended use. In a loan whose contract required a nine-month rate, the parties agreed to create a synthetic fixing by taking the arithmetic midpoint of the observed six-month and twelve-month rates. The example arose after publication of the nine-month tenor stopped, while the contract’s fallback language would otherwise have reused the last available fixing.
The responses describe linear interpolation between nearby tenors as a common practical choice for client needs, while pointing to arbitrage-free interest-rate interpolation as a more model-conscious alternative. The loan example is a negotiated contractual solution, not evidence that the midpoint is suitable for every valuation or trading purpose. Interpolation can introduce arbitrage or modeling issues in other contexts, and the document does not derive or compare methods quantitatively.
Key ideas
- The appropriate interpolation method depends on the contract or valuation use of the missing tenor.
- A loan’s synthetic nine-month fixing was set to the arithmetic midpoint of six-month and twelve-month rates.
- Linear interpolation is described as a common practical approach when clients need an unavailable tenor.
- Arbitrage-free interpolation methods may matter for uses beyond a specific contractual agreement.
- The example does not establish a universally appropriate interpolation rule.
Tags
Full text
# Interpolating Libor 9M rate? # Interpolating Libor 9M rate? Libor atm is: ``` 3M = -0.54486 % 6M = -0.52514 % 9M = 1Y = -0.47443 % ``` How to retrieve the 9M Libor rate? ## Answer by Dimitri Vulis (score 6) https://quant.stackexchange.com/a/59179 It depends on what you want to do with the interpolated 9M rate. For example, I encountered this practical problem once. Desk loaned some money to an agricultural firm that, for liquidity reasons, wanted to pay interest like this: - a coupon with 9 months worth of interest, reset from 9M USD LIBOR + spread - 3 monthly coupons reset from 1M USD LIBOR + spread - another 9-month holiday, followed by 4 floaters - repeated for several years. Everyone was happy until, a few years into this, they unexpectedy stopped publishing 9 months tenor (circa 2013). The language in the loan documents literally meant the latest available 9M LIBOR would be re-used until the maturity. Neither party liked that. The lawyers spoke and agreed that for this loan, a synthetic 9M LIBOR would be linearly interpolated from 6M and 12M tenors (that were still being published) - just the arithmetic mean, 1/2 of each of the 2 observable tenors. No one cared whether this linear interolation, if used in other contexts, might admit arbitrage or lead to other problems not relevant to this loan. Any more complicated interpolation would add no value to either party and would confuse the lawyers and the customer. ## Answer by rvignolo (score 1) https://quant.stackexchange.com/a/59181 I would recommend reading: Erik Schlogl, Arbitrate-free Interpolation in Models of Market Observable Interest Rates. Andersen and Piterbarg, Interest Rate Modeling, Chapter 15. Finally, this Masters Thesis is really nice. ## Answer by ZelliZello (score 0) https://quant.stackexchange.com/a/59182 Speaking for USD, people stay away from tenors other than 1M, 3M, 6M, and somehow 12M. And if any client has a need for a different tenor, almost always will a linear interpolation between the closest tenors be used. 12M libor is still published but not a lot of new contracts are indexed on it. Someday some 12M libor swap might trade in the interdealer markets but it is more inventory-management related than flow related.
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