LMM Swaption Calibration and Forward-Rate Convexity Adjustment

Summary

The document describes a calibration problem in a Libor Market Model. The author simulates forward-rate paths with Euler steps, computes swaption rates, and aims to calibrate correlations among the Brownian motions. They report that subtracting a term involving consecutive forwards and their rank seems necessary to fit market swaption volatility, and ask whether this is a convexity adjustment.

The question reflects uncertainty about how the model’s measure affects simulated rates and calibration. It supplies no answer, equations, calibration results, or sufficient implementation details to determine whether the adjustment is appropriate. In particular, it does not specify the exact measure, rate definitions, swaption valuation procedure, or volatility convention. It is therefore a useful pointer to a modeling issue, but not a validated calibration recipe.

Key ideas

• The author uses Euler simulation of forward rates in an LMM to obtain swaption rates.
• The stated calibration goal is to infer correlations among the model’s Brownian drivers.
• An unexplained adjustment involving neighboring forward rates appears necessary to fit market volatility.
• The document does not resolve whether this term is a convexity adjustment or provide enough detail to validate the procedure.

Tags

# Problem fitting LMM to swaptions


# Problem fitting LMM to swaptions












I don't know what I am doing wrong. My goal is to calibrate correlations between my brownian motions. For that I simulate forwards paths and then calculate Swaptions rates.

I use Euler Method to simulate my forwards rates. Once done, I need to substract my convecutive forward multiplied by their rank to have a correct fit and I don't understand why. It looks like some kind of convexity adjustement is needed to fit bbg volatility.

But my understanding is that the LMM is supposed to put the forwards in the correct measure.

Do any of you already came accross this problem?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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