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I have price a IRS receiver fixed rate, and I am told to approximate the PV of IRS with a long fixed rate bond, with coupons assigned by the swap rate and face value equal to the IRS notional, and a short cash position with same amount as the IRS notional. then I am told that fixed rates are annual with coupons semi-annual. in order to find the price I compute $NPV^{fixed}-NPV^{floating}$ where the floating is $1-B(t_0,T)$ anche the fixed is $S$ because of the sum of discounted rates every semester. $S$ is the annual rate.

Is it correct to consider $S$ or I should consider $S/2$?

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Fabio Ambrosini is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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The fixed rate of a swap is $X = (DF_0-DF_N)/dv01$, where $dv01 = \sum_i^N (Daycount_i*DF_i)$. Here $DF_i$ are zero discount factors (so $DF_0=1$ for a spot starting swap) and $Daycount_i$ are the day count fractions on the FIXED LEG of the swap. So in your case $Daycount_i = 0.5$ for semi-annual coupons. X is an annualised rate i.e. the fixed leg coupons will be Nominal*0.5*X.

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user35980 is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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