# Pricing a swap

I have a doubt as to why this concept wont work for valuing a swap, X days after initiation. Shall appreciate anyones help. To me if a swap was priced to be zero at initiation at a rate of R1 and then we need to value it after X days. Then conceptually it should be the same as valuing a new swap as if its initiating on day X (with new LIBOR rates) and then attributing the difference as value to the fixed rate payer. Consider valuing a swap to the fixed rate payer. Plugging in the the numbers from Schweser page 284. The plain vanila swap was priced at 6.052% at initiation when the 90day libor was 5.5%. Now we have to value this 30days after initiation when Libor is R60 = 6, z1 = 0.99010 R150 = 6.5, z2 = 0.97363 R240 = 7, z3 = 0.95541 R330 = 7.5, z4 = 0.93567 Applying the above concept - Calculating the fixed rate at swap initiation (day 30) as - 1- Z4/ (sum Zn) = 0.0166% = 0.0166*100*360/90 = 6.6752% So had the fixed rate payer entered into a swap at day 30 he would have had to pay 6.6752% anually. Instead he is only going to pay 6.052%. So the difference is his profit or price of swap ! In this case the notional principal was 30m. So the value = 30m * (6.6752-6.052)*90*100/360 = 46747.24. I understand Schweser’s methid of doing this but find this simpler…what am I missing :((( thanks.

I think the above method is normally used for value calculation of swaptions. As far as swap value calculation is concerned this method will not give you the desired result because the new swap rate = 6.6752% is calculated assuming the floating rate bond is at par value. But the floating rate bond 30 days after swap intitiation is more than the par value. I think this leads to the difference in the answer. You can still use the above method but then you will have to add the difference between the floating rate bond and its par value to your calculation. It should roughly give you the same result as given in schweser.

if you ran used ozaj’s method on the next reset date for the floater, when it resets back to par, that SHOULD work, theoretically