Calibrating a LIBOR Market Model to Price Floating Notes

Summary

The document considers how accurately a forward LIBOR market model should price portfolios of derivatives designed to replicate floating notes, including portfolios containing complex Bermudan products. The key guidance is that matching swaption prices calibrates the model’s volatilities, but does not by itself ensure that the model reproduces floating-note values.

The answer says floating notes, or comparable instruments such as swaps, are needed to obtain appropriate drifts. A model intended for pricing more exotic products should first be able to replicate floating-note prices exactly. This serves as a model consistency requirement and a practical check before relying on the model for complicated hedging portfolios. The response offers no quantitative accuracy estimate, calibration recipe, or empirical evidence; its conclusion is a validation principle rather than a guarantee that correct floater pricing ensures accurate exotic pricing.

Key ideas

• Swaption calibration determines model volatility inputs but is not sufficient to ensure correct floating-note prices.
• Floating notes or comparable instruments such as swaps are needed to set appropriate LIBOR model drifts.
• A valid model should reproduce floating-note prices before it is used to price more exotic products.
• Exact replication of simple instruments is a consistency check, not a stated guarantee of exotic pricing accuracy.

Tags

# How accurately can the LIBOR market model price a floating note


# How accurately can the LIBOR market model price a floating note












I am considering some hedging strategy where portfolios of derivatives are built so that each portfolio is equivalent to a floating note, even if the instruments in the portfolio might be quite complicated, e.g. bermudean snowballs.

I plan to price numerically these portfolios in a forward LIBOR market model calibrated to swaption prices and I am wondering which accuracy I should expect on the total portfolio prices, i.e. on the pricing of floater notes.

## Answer by Juan Ignacio Gil (score 2)

https://quant.stackexchange.com/a/9622

Calibrating to swaption prices would give you the right volatilities for your model, but you have to use the floating notes (or similar instruments, as swaps) in order to get the right drifts. In any case, your model have to be able to exactly replicate the floating notes prices in order to be considered a valid model, and you can feel comfortable to use it with more exotic products.

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