Why One-Factor Hull–White Cannot Generally Fit Floors and Swaptions

Summary

The document asks whether a one-factor Hull–White interest-rate model can price a European swaption that includes a floor on its floating leg while matching both swaption volatility and LIBOR volatility. The response says that fitting the floor or cap market can leave model swaption prices too high relative to market prices, so both instruments generally cannot be calibrated consistently with this model setup.

The stated reason is the model’s limited treatment of dependence across the yield curve. The price difference between swaptions and cap or floor instruments depends chiefly on expected decorrelation among different parts of the curve, which a one-factor structure does not represent. The suggested remedy is a richer specification, such as a multifactor model or a term-structure model. The answer is brief and offers no calibration procedure, market example, or quantitative evidence, so the conclusion should be understood as a modeling limitation described at a high level rather than a complete pricing analysis.

Key ideas

• A one-factor Hull–White model may not fit cap or floor prices and swaption prices at the same time.
• The mismatch is attributed chiefly to missing decorrelation across different parts of the swap curve.
• A multifactor or richer term-structure model can represent more curve dependence.
• The response gives a qualitative limitation rather than a detailed calibration method or numerical demonstration.

Tags

# How to prrice a European swaption with floor?


# How to prrice a European swaption with floor?












I'm wondering how we can price a european swaption with a floor on the floating leg. Assuming that we use the HW 1 factor model, how we can simultaneously calibrate the swaption ( on swap rate volatility) and the floor (on the libor volatility).

Do you have any idea how to do this?

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/31646

You can't. In a 1 factor model, if you calibrate the libor floor to market, then the swaption prices in the model are likely to be too high versus the market. That's because the difference between swaption prices and cap/floor prices is determined chiefly by the expected decorrelation between different parts of the swap curve , which is not present in the model. You need a richer model such as a multifactor and/or term structure model in order to achieve this.

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