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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 ?

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  • $\begingroup$ It is a huge project to do everything from the ground up. What tools do you have now? Do you have access to Bloomberg? $\endgroup$
    – Alex C
    May 4, 2018 at 16:01
  • $\begingroup$ I know it a huge project should it start from scratch. We have have a scripted MC solely dedicated to equity/fx (variance/vol) derivatives, with mainly a 3F displaced BS/SABR and local vol. Nothing for rates. We do have BB terminals, but really want to have an in-house pricer. $\endgroup$
    – Olórin
    May 4, 2018 at 16:15
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    $\begingroup$ Practically I would start with a BGM, and then will complicate when needed and when the BGM would be in PROD. At least to price stantard (non fwd vol dep) LIBOR derivatives first etc. $\endgroup$
    – Olórin
    May 4, 2018 at 16:17
  • $\begingroup$ @AlexC In fact, I am wondering about what I could do with BB's vol cube and trying to keep it simple. $\endgroup$
    – Olórin
    Feb 20, 2019 at 16:58

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