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Choosing a Multi-Curve Model for Swaptions Across Tenors and Settlement Types

Article Quant Q&A · Author: Olórin
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Summary

The document frames the model-selection problem for pricing vanilla swaptions on fixed-versus-floating or floating-versus-floating legs. Requirements include multiple floating-rate tenors, OIS and LIBOR legs across currencies, mid-curve structures, and both cash and swap settlement. The proposed use case also calls for consistency with basis and cross-currency basis swap calibration and potentially pricing other interest-rate derivatives.

A large stochastic-volatility LIBOR market model is raised as a possible approach, with the recognition that intermediate-maturity swaptions can depend on forward swaption volatility. The document is a question rather than a resolved modeling recommendation: it gives no comparison of candidate models, calibration results, implementation guidance, or validation evidence. Model suitability would depend on the instruments and markets to be covered, calibration quality, and the practical complexity the desk can support.

Key ideas

  • The requested framework must accommodate multiple floating-rate tenors and currencies.
  • The pricing scope includes OIS and LIBOR legs, mid-curve structures, and cash or swap settlement.
  • Calibration to basis and cross-currency basis swaps is part of the stated multi-curve requirement.
  • A stochastic-volatility market model is proposed as a candidate, but the document does not establish that it is suitable.

Tags

OptionsFixed incomeDerivatives pricingVolatility
Full text
# The "I want to price swaptions" request


# The "I want to price swaptions" request












In a small buy-side structure I recently had the following request : "I want to trade swaptions, I need to price them".

After a quick discussion the need is to price vanilla options on fix vs float or float vs float legs where float leg can either be

- OIS floating leg (that is, the floating leg of an OIS swap)

- LIBOR (different currencies allowed) floating leg

In case of real swaptions, they can be mid-curve or not, and can be either cash or swap settled, depending on the currency. (I personaly wouldn't want to use the old standard market trick to price a cash settled swaption with a model calibrated to swap settled swaption but anyway ... This just to say that ideally the model I am looking for should handle swap and cash settled swaptions ...)

I am asking myself : how to proceed ?

First I could have different models per tenors but as I could have to price for instance an option on USD 6M LIBOR floating leg vs a GBP 3M Libor floating leg, I would need a "multi tenor" model at least, model that would be calibrated on basis swaps and on cross currency basis swaps so that at the end, I would prefer to have a model handling all tenors etc.

Is there a general model doing this ? Like a huge LMM with stochastic volatility ? (Typically mid term swaptions care about forward swaption volatility.)

Other constraint : my structure is not that much strong in the rate derivatives business so that it could be good that the model could price other rates derivates as well.

Is a big LMM with stochastic vol (heston for instance) with basis and cross currency feature a good idea ?

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.