hello, Id like to compute the Delta of a Swaption. I've read some other posts on the subject here, but I guess I don't follow the exact calcualtion.Suppose I have a $100 notional 1Y5Y swaption, and I want to hedge it with the underlying fwd 1Y5Y swap. then, assuming Im usign black's model for pricing the swaption, is the delta:delta = (swaption_1 - swaption_0 )/(swap_1 - swap_0) where swaption_0 and swap_0 are the PV of the swaption and fwd swap, and swaption_1 and swap_1 are the PV's after bumping the curve by 1 bp. If i do this I get close, but not exact the bberg's calculation, so I think I must be misunderstanding something. Any thots?thnx.

I think you want to calculate dP/dr of each security separately . . . For each security, dP/dr = (P(r+1bp) - P(r-1bp)) /2bpAlternatively, you can do dP/dr = (P(r+1bp)-P(r))/ 1bp, but it isn't as good of an estimate. Once you have dP/dr of both securities, your "delta", isdelta = dP/dr of swaption / dP/dr of swap.Hope this helps (and hope I didn't screw anything up!).

yes, that makes perfect sense. thnx !

QuoteOriginally posted by: mabroe hello, Id like to compute the Delta of a Swaption. I've read some other posts on the subject here, but I guess I don't follow the exact calcualtion.Suppose I have a $100 notional 1Y5Y swaption, and I want to hedge it with the underlying fwd 1Y5Y swap. then, assuming Im usign black's model for pricing the swaption, is the delta:delta = (swaption_1 - swaption_0 )/(swap_1 - swap_0) where swaption_0 and swap_0 are the PV of the swaption and fwd swap, and swaption_1 and swap_1 are the PV's after bumping the curve by 1 bp. If i do this I get close, but not exact the bberg's calculation, so I think I must be misunderstanding something. Any thots?The delta you are computing is the out-of-the-model delta. The delta can also be computed in-the-model which is equivalent to the N(d_1) in the Black and Sholes model. The two figures are somehow similar but not equal. You should check which one Bloomberg is using.You can find more details about swaption delta in a recent Wilmott magazine technical article (November 2005): Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas.

Hi, ericlambi:dP/dr = (P(r+1bp) - P(r-1bp)) /2bp, r means swap rate, right?

or r means the forward rate?