Fitting a Nelson-Siegel Curve from Coupon Bond Prices
Summary
The document discusses preparing bond data to fit an extended Nelson-Siegel-Svensson yield curve. The response cautions that yield to maturity may be unsuitable for callable bonds, especially when the call is economically relevant; yield to worst may better reflect the relevant redemption outcome. It also advises using maturity dates at day-level precision rather than rounding them to months, which can add noise.
For coupon-bearing bonds, the suggested procedure is to use the dirty price, including accrued interest, and projected coupon and principal cash flows, then solve numerically for the yield that equates discounted cash flows to that price. The response notes that market conventions can affect the calculation, including compounding conventions for longer-dated zero-coupon bonds. It does not specify a complete curve-fitting procedure or conventions for a particular bond market.
Key ideas
- Check whether bonds are callable before relying on yield to maturity; yield to worst may be more relevant.
- Use precise maturity dates rather than rounding maturities to months.
- Calculate coupon bond yield by solving for the rate that discounts projected cash flows to the dirty price.
- Bond-market conventions, including compounding rules, can affect yield calculations.
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Full text
# Building a Nelson-Siegel curve # Building a Nelson-Siegel curve 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 - Is it correct to use the YTM? - Is it correct to graph it vs. the maturity in months? - 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. ## Answer by Dimitri Vulis (score 2, accepted) https://quant.stackexchange.com/a/68880 > 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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