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Recently I got some question about Spot Curve which is extracted from Swap rate.

And the logic starts with this : Fixed rate bond's value is equal to Floating rate bond's value "at reset date"

please, see below picture. enter image description here

c is swap rate, Z(0,T_j) is Discount Factor start from zero to T_j, n is payment frequency

However, I searched past questions which are same for my question on this 'Stack Exhange' then I found that most of them use this logic when it is not reset date!

Why we use par yield concept although it is not reset date?

What I think is : Because it is not reset date, the equation (5.42) above picture should be modified. That is the 100(par value) should be some Number which is present value of Floating Rate Note.

And the Floating Rate Note's value is should be not Par when it is not reset value except for when the discount rate is coupon rate. But how can we be sure of that? It depends future condition.

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