Swaption: Cash and Physical settlement

NY153 · November 2nd, 2005, 7:49 am

Hi everybody,I have to evaluate a chooser swaption: at the expiry I decide whether to deliver in cash or physically.The difference would be very small but would be a bet on the yield curve inversion. Isn’t it?Therefore it would need a 2F IR model, isn’t it?Any experiences or comments are welcome.Thanks,N.

vegavexity · November 8th, 2005, 12:36 pm

Cash vs. Physical is a credit issue.. If the expiry is executed properly (i.e. the traders knows what he is doing) there is no vaulation issue at all. Steep, flat or inverted curve shouldn't matter. All the value in the underlying swap would be picked up in the unwind/cash value at expiration. The whole idea behind a cash settlement is that you can ignore the credit of your counterparty and go out and do the same transaction in the market at no cost isn't it....

piterbarg · November 8th, 2005, 4:26 pm

It depends on the definition of the "cash" delivery, it means different things inhe US and Europe. In the US, a cash settled swaption pays the cash value of the underlying swap and thus Vegavexity is correct. In Europe cash-settled means the same as yield-settled in the US, where you compute the cash value by discounting the swap cashflows at the realized swap rate. Then NY153 is right and you need some sort of model to value the difference between the two-V

vegavexity · November 8th, 2005, 5:16 pm

What do mean when you refer to the "realized swap rate?"The "the cash value by discounting the swap cashflows" at current market rates will give you the cash value of the swaption, so I presume that the realized rate is something other than the current one. Perhaps the rate on the swaption?

BahamianMan · November 8th, 2005, 7:15 pm

@vegavexity : What do mean when you refer to the "realized swap rate?"I think piterbarg is refering to the fixing rate.In Euro all the cash flows are discounted at that rate, thus at a flat yield curve, while the physicaly delivered swaption depends on the slope.Hope it helps

akimon · November 8th, 2005, 10:35 pm

Your cash settlement amount on a payer swaption would be = ( Spot rate at settlement date - Strike of Swaption) * Notional * PV01 swapThe PV01 is model dependent, depending on the way you construct yoru curve you will get every so slightly different valuesIn EUR swaptions your "settlement PV01" is calculated assuminging a flat yield curve on settlement date, where every rate is the swap rate, and your PV01 is just discounted with a constant rate, so that every dealer can agree on the fixed settle amount and that amount will not be booking-system dependent.

caroe · November 10th, 2005, 7:45 am

In fact, the ISDA definitions have (I believe) 4 different definitions of "cash settlement" to account for the differences between US and European style cash settlement - although couched in legal terms that makes quite a difficult read for mathematically inclined persons...