Normally to calculate swap I would go step by step, PV of fixed payment , PV of floating payment

In question 43 to calculate RECEIVER SWAPTION, can anyone please explain the rationale for it, especially why they subtract 0.969 from return of index (15%)?

P/S: Do you usually do quick way like this or you would go step by step to make sure you dont miss anything ( but chance of mistake increase)

43 is an equity swap not a swaptionâ€¦They state that under the terms of the swap they receive the return on the index and pay fixed. They are doing the return of the index - the fixed payment.

The return on the index is the fraction like you said and then they subtrace the fixed which can be written

- [.012 * (.9976+.9924+.9861+.9696) + 1*.9696] but they for some reason distribute the negative and reorder the terms.

Now I got the rationale behind but still, why they subtract 0.969 from return of index (15%)?? 0.969 is discount factor for 720 days . Thought the floating rate payment need to be discount using 180 days rate? Anyone?

there is no floating - it is the equity return vs the fixed

the -.969 is the second term i wrote for the fixed - the 1 * ,969, it is the pv of the principal

.9696 is the z4 . it is 1/(1-(.0342^(330/360)))

Oh thanks. But I thought equity return is considered Floating rate?

oh ok, i meant that there wasnâ€™t the traditional floating thing, it was an equity return.

The equity return is just the fraction, nothing else, just the single term