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1

Almost both ;-) If R is the spot 30 year yield, then: $NPV = \frac{coupon}{(1+R)^{t}}$, summed from $t=0$ to $t=30$. This is almost the same as your second specification, albeit you do need to discount the coupon in year 20 by more than that in year 2. And it's the one they'll teach you as the standard model on any course. But there is also an ...


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The value of the bond would be the first case, because you have to discount each cashflow with the relevant spot rate for that payment date. Although, because rates are normally expressed in annual terms, you would have to adjust for the days: $(1+R)^{n}$ or $(1 + R \times n)$ What you might be confused with, is the yield of the bond, which would be the ...


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To answer the questions in your comment: What is a 3M swap rate? Either it's a fixed rate vs a shorter tenor (ex:1m) or a fixed rate vs the same tenor but forward (in this case a FRA), or if it's starting spot then it's the same as a zero rate because it has to intermediate payments. The floating rate conventions are in the definition of the floating index. ...


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Maybe you should start with a simple example, because you have so many moving parts that it's hard to figure out where the difference is. Most likely some different convention between your helpers and the instruments you are trying to price. import QuantLib as ql today = ql.Date().todaysDate() calendar = ql.TARGET() spot = calendar.advance(today, 2, ql....


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