# price of IRS receiver fixed rate [closed]

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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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.