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I originally posted this on Mathematics, but was told my question is better suited here.

I want to graph a yield curve with an extended version of the Nelson-Siegel-Svensson. I have the issue date, the due date, the periodicity, the coupon rate and the price of 37 bonds. I have assumed I must calculate the yield to maturity and graph it versus the maturity in months. To fit the curve with the data I have used R functions. My questions are

  1. Is it correct to use the YTM?
  2. Is it correct to graph it vs. the maturity in months?
  3. Assuming the answer is yes, I have some zero coupon bonds, for which the YTM function is relatively simple, but how do I properly get the YTM for couponed bonds? I've been using a very simple approximation but I want to be more formal. The information I have read has been very confusing on the matter.
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  • $\begingroup$ In their paper, hey call the object being interpolated yield to maturity as you have stated. But if you look closer at p475 of their paper, you see that they may be modelling spot rates instead of the thing we commonly call yield. IMHO, the distinction does not matter as long as the fit is good and the resulting model is sensible. $\endgroup$ Nov 23, 2021 at 7:57

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Is it correct to use the YTM?

Maybe. These days, for accounting reasons, a lot of bonds out there are callable, and the call is in the money, and the YTW is very different from the YTM. You should check whether your bonds are callable before assuming that you can use YTM.

Is it correct to graph it vs. the maturity in months

You introduce unnecessary noise by rounding your dates to months instead of days.

how do I properly get the YTM for couponed bonds?

If you know the bond's dirty price (= clean price + accrued), and the projected cash flows (coupons and principal), then you solve (numericlaly, iteratively) for the yield that makes the discounted cash flows equal to the dirty price. There may be further market conventions for your bonds. For example, if you have zero-coupon bonds maturing in more than one year, then usually the conventional yield is calculated assuming annual compounding, rather than the closed-form formula you may have in mind.

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