The swaption can be either swap settled (which is the default convention) or cash settled. When pricing them, Is there any difference? Assume that we do not need to consider credit charge. I do not see any difference. But someone told that they differs.

In order to compute the currency premium of the swaption, you need to calculate the Basis Point Value.This BPV will change wether you use Cash or Physical/Discount Cash settlement.

QuoteOriginally posted by: dollaryenThe swaption can be either swap settled (which is the default convention) or cash settled. When pricing them, Is there any difference? Assume that we do not need to consider credit charge. I do not see any difference. But someone told that they differs.There is a difference in valuation.In the book of Brigo and Mercurio there is a simple adjustment for valuing cash-settled swaptions which some people use.

Cash settlement of swaptions means that no swap is entered between the two counterparties when (if) a swaption is exercised, instead a cash payment equal to the swap value is exchanged. Hence you need a way to determine the market value of this swap. In EUR, market convention is to use a flat rate equal to the swap rate for the swap in question and use this for discounting swap payments. This makes life easier for the two counterparties, as you only have to agree upon a single swap rate (e.g. using the ISDAFIX2 Reuters page) instead of a complete set of discount factor (or, in the worst case, a set of deposits, futures and swap plus a yield curve bootstrapping method!). In USD matters are different. The ISDA definitions lists the various possibilities for cash settlement methods, although couched in the usual legal mumbo-jumbo lingo.

For US swaptions it should make no difference to the valuation of the option because you settle the PV of the swap for cash using a full swap curve.As has been stated for GBP and EUR you use the reference swap rate to work out a flat discounted amount.This has no effect on valuation of 1 year swaptions or where the curve is flat. It has the largest effect on trades where the maturity of the swap is long and the curve is steep, as the forward curve tends to be fairly flat in most currencies it tends to have the largest effect on short dated options onto long dated swaps.In an upward sloping yield curve the PV01 of a swap is > the PV01 calculated using a flat yield, therefore the swap settled option is woth more.In a downward sloping yield curve the PV01 of a swap is < PV01 using a flat yield curve, therefore cash settled option is worth more.

Yes caroe is totally correct, just to help the orignal poster some more:Suppose R% is the fixing on expiry and you have a swaption into a n year swap with m coupons per year. Then the discount factors are 1/(1+R/m)^i for i = 1, ..., mn.