Calibrating an LMM to One-Year Swaptions for a Three-Month LIBOR Autocap

Summary

The document considers pricing an autocap, a cap-like contract that automatically exercises in-the-money caplets but limits how many can be exercised. Since its value depends on correlations among LIBOR rates, the author proposes calibrating a LIBOR Market Model (LMM) with swaption data, following a cascade calibration approach described in an interest-rate modeling text.

The practical obstacle is that the author can obtain volatility data only for one-year swaptions. They ask whether calibrating the dynamics of one-year forward rates and interpolating those dynamics to three-month forward rates is appropriate. The document provides no pricing results, calibration details, or assessment of the proposed interpolation. It therefore identifies a model-data limitation and an open methodological question rather than establishing that the approach is sound. A useful evaluation would need to consider whether the available swaption instruments sufficiently constrain the relevant rate volatilities and correlations for the autocap's tenor and payoff.

Key ideas

• Autocaps limit the number of caplets that may be exercised while requiring exercise when a caplet is in the money.
• The contract's value depends on correlations among LIBOR rates.
• The author proposes calibrating an LMM to swaption volatility data using a cascade approach.
• The available data reportedly cover one-year swaptions, prompting a question about extending the calibration to three-month forward rates.

Tags

# Price 3m libor autocap with LMM calibrated on 1y swaption data


# Price 3m libor autocap with LMM calibrated on 1y swaption data












I need to calculate a price of an autocap contract which is

> An autocap is similar to a cap, but at most γ ≤ β caplets can be exercised, and they have to be automatically exercised when in the money

Payoff is

This product heavily depends on correlation between libor rates. Therefore to incorporate this information into model, I decided to use cascade calibration approach described in Brigo and Mercurio book "Interest rate modeling" - I want to calibrate LMM to swaptions. The problem is that as I understand, only volatility of 1Y swappoints can be derived from Bloomberg. So I'm able to calibrate only 1Y forward rates dynamics. Then I'd like to use some interpolation approach to get from 1Y forward rates to 3m forward rate.

Is it a good idea?

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