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prodiptag
Topic Author
Posts: 124
Joined: September 12th, 2008, 4:41 pm

### midcurve swaptions

If we have an ATMF midcurve swaption straddle position, one way to replicate this is via a long and short straddle, the strikes being the respective ATMF strikes. What if the original midcurve is quite OTM, any idea how to split the strikes of the long/short straddles combo - preferably in as much model independent way as possible?

mathmarc
Posts: 202
Joined: March 18th, 2003, 6:50 am

### midcurve swaptions

QuoteOriginally posted by: prodiptag If we have an ATMF midcurve swaption straddle position, one way to replicate this is via a long and short straddle, the strikes being the respective ATMF strikes. What if the original midcurve is quite OTM, any idea how to split the strikes of the long/short straddles combo - preferably in as much model independent way as possible?What do you mean by "midcurve swaption"? Is this by extension of the STIR future jargon an option on a swap that starts 1 (or 2) years after its expiry?If this is the case, it can not be treated as long (the full period) and short (the period up to start). That is correct at the swap level, not at the swaption level. The basket of option (long/short options) is not equal to the option on a basket (midcurve swaption). The long/short options give you an upper bound on the price of your midcurve, not an unbiased estimate of the price itself.The only way I know off to price this type of deal is to use a multi-factor model and to calibrate it to the two option you mentioned. It is important to use a multi-factor model, as described in [Hunt and Kennedy. Financial Derivatives in Theory and Practice. Section 15.4], as a single factor model will always be an upper bound for the price. Often those options are treated as special cases of non-constant notional swaption. Calibrating to the two options you mentioned gives you hedge ratios with them, but the ratios are dynamic, not static.This does not really answer your question on how to split the strikes. The answer to this question is also required as an input to the calibration basket.You can also use a multi-factor with smile model (like LMM-SABR) and you don't have the question of the calibration, as the model "calibrate the full market", but you still have the question of the hedging instruments.I hope this help.

prodiptag
Topic Author
Posts: 124
Joined: September 12th, 2008, 4:41 pm

### midcurve swaptions

thanks for your answeryes i know they are not equivalent, and I am not looking for a pricing method, there are loads actually, more was talking about hedging. Practically, for a mid curve swaptions, I would take some position on the long/short straddle partially, and hedge the rest of gamma and hope the realized correlation is not too off against me from my pricing marks. To do that, the choice of strikes are obvious for an ATMF midcurve. Was wondering what are the thoughts doing the same for off the money, in case of anyone has tried this in practice

prodiptag
Topic Author
Posts: 124
Joined: September 12th, 2008, 4:41 pm

### midcurve swaptions

and another reason I am looking for this to create a synthetic position in forward vol. One way to do that is to buy a calendar and then sell a fly on the shorter expiry - to take care of the possible losses from the short gamma in the calendar in a large move. While this works okay on longer tails, for the shorter tails it does not. Because there, the midcurve impact becomes important and a calendar is simply not a position in forward vol. So it should be a long straddle vs a atmf midcurve, and then a short midcurve fly. Now dealers don't quote midcurves sweet (and of course not forward vol). So replicating them is an options. Now I can replicate the atmf midcurve, but it beats me how to do that for the midcurve fly in a smart manner

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