Normal Libor Market Model: Skew Fit and Zero-Floor Limitations

Summary

The document describes practical experience with a normal Libor Market Model as an alternative to a shifted lognormal model. In a higher-rate environment where receiver options were more expensive than comparable payer options, the normal model’s symmetric skew was said to fit market prices more closely than the lognormal model. It also assigned nonzero value to zero-rate floors, although that was incidental to its use.

When rates moved close to zero after the financial crisis, the market skew shifted toward more expensive payers, reflecting a heavy right tail. The respondent reports that the normal model then miscalibrated the skew and overstated the value of zero floors, prompting a move away from it. This is a single practitioner’s historical account, not a comparative calibration study. The central limitation is that a normal distribution may suit one skew regime but fit poorly when rates are low and the market distribution is strongly asymmetric.

Key ideas

• A normal Libor model can fit symmetric market skew better than a lognormal model in some rate environments.
• The model assigns value to zero-rate floors as a consequence of its distributional assumptions.
• Near-zero rates and payer-favoring skew can make the normal model miscalibrate option prices.
• In the described experience, the model overstated zero-floor value when rates were low.
• Model suitability depends on the prevailing rate level and the shape of market skew.

Tags

# Normal Libor Market Model


# Normal Libor Market Model












Is anybody using normal Libor Market Model (LMM) (as opposed to shifted lognormal LMM)? It could be one of the approaches to dealing with negative rates. If you do, have you encountered any theoretical or practical difficulties with it? Thank you.

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/37935

Yes I used one in the early 2000s. At the time, US interest rates were quite high (5 or 6pct) and the market skew was such that -100bp receivers were more expensive than +100 payers. The lognormal model is very inappropriate for this skew regime , but the normal model is much closer, having symmetric skew. As a byproduct of this we noticed that the model put nonzero values on zero floors, but it was not the main purpose.

When rates rallied close to zero following the 2008 crisis , we had to migrate away from the normal model because the market skew became heavily payers-over-receivers, due to a heavy right hand tail. That is the main theoretical problem. When rates are low , the normal model miscalibrates the skew. When rates are low it also places too high a value on zero floors compared to the market , in my experience.

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