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 ?