Estimating Zero Coupon Curve using only Fixed-Coupon bonds available

External question — Quantitative Finance Stack Exchange Author: Monchinga Original post: https://quant.stackexchange.com/questions/71590 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Today I have been struggling with something that someone here for sure has already encountered. I have a corporate issuer with a set of fixed coupon bonds (maturities between 1.5 to 20+ Years, luckily same coupon frequency), and I would like to estimate a Zero-Coupon Curve out of it. However, this is not like the dummy exercises at university where you always have a zero coupon bond as a starting point, regular intervals between maturities (i.e. 0.5, 1, 1.5y, etc...) and you can build it easily. Is there any technique that can be used to achieve such a goal? I have briefly read about a "Nelson-Siegel" approach, but I could not understand if such a model can accommodate coupon bonds or if I need zero coupons to estimate the coefficients. I'd be very grateful if anyone could help me. Many many thanks

External answer — Quantitative Finance Stack Exchange Author: Chris Edmonton Original post: https://quant.stackexchange.com/a/71649 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. You can model the issuer's yield curve using either whole-curve models (such as Nelson-Siegel) or piece-wise cubic polynomial models. You could consider instead modeling the issuer's z-spread curve by interpolating the issuer's bonds' z-spreads (over government or swap curve) using a simple smoothing technique. The Nelson-Siegel method would definitely work for a set of single-issuer corporate bonds of uneven maturities. If you have access to the source code of an implementation designed for par-priced round-maturity bond-or-swap benchmarks (several are in the public domain), you could adapt it as follows: at each iteration of the optimizer used to fit the parameters, use the new curve to price the set of bonds (discounting their cash flows, adjusting for accrued interest), then calculate their yields (using their price-to-yield function), and then calculate their yield error to market yields; the optimizer should target the minimization of the vector of yield errors on the set of bonds. As you likely know, as some bonds of a given issuer tend to trade rich/cheap (e.g., due to illiquidity or discount/premium), they may distort the issuer curve. To avoid such distorsions, you may choose to adjust these bonds' market yields with subjective spreads prior to curve estimation.