Imagine that you have a pay fixed quarterly SWAP and receive the returns on an equity index (quarterly). The discount factors, rates and else are given below. Lastly, this is a one year SWAP initiated 30 days ago.

Fixed pay: .01 on notional 60M

Index receive: index was at 900 at initiation, now, 30 days later it is at 1000. Notional is 60M

Discount factors: Z1(60day) = .99, Z2(150) = .98, Z3(240) = .97 and Z4(330) = .96

I realize that on a $1 of notional, the value of the SWAP to the fixed payer is:

= (amount received from equity index) - (amount paid fixed)

The answer I see for this question is as follows:

= ((1000/900) - .96) - (.01 * (.99 + .98 + .97 + .96)

The pay fixed portion makes perfect sense. The only part that I’m a bit dubious about is regarding the subtracting of Z4 frin 1000/900. I have not seen this before and just want to get your opinion if this is a correct way to ‘discount’ the equity index returns to the end of the year.

Thanks