Fitting a Corporate Zero-Coupon Curve from Coupon Bonds
Summary
The document explains how to estimate an issuer’s zero-coupon or discount curve when the available instruments are fixed-coupon corporate bonds with uneven maturities. It presents whole-curve approaches such as Nelson–Siegel and piecewise cubic curves, and suggests interpolating bond z-spreads over a government or swap curve as a simpler alternative.
For a Nelson–Siegel fit, the described procedure repeatedly uses candidate curve parameters to discount each bond’s cash flows, accounts for accrued interest, converts model prices into yields, and minimizes the errors against observed market yields. The approach can accommodate bonds that are not par priced and do not mature at regular intervals. The document offers no empirical comparison of the alternatives or detailed implementation choices, so the results will depend on model specification and input quality. It also cautions that bonds trading rich or cheap because of liquidity or price effects can distort the fitted curve; subjective yield adjustments are suggested as one possible mitigation.
Key ideas
- A corporate curve can be estimated from coupon bonds even when maturities are irregular.
- Nelson–Siegel and piecewise cubic models are possible whole-curve approaches.
- A fitted curve can be assessed by repricing cash flows and minimizing market-yield errors.
- Interpolating issuer z-spreads over a government or swap curve is a simpler alternative.
- Rich or cheap bonds can distort the estimate, and yield adjustments may be considered.
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# Estimating Zero Coupon Curve using only Fixed-Coupon bonds available # Estimating Zero Coupon Curve using only Fixed-Coupon bonds available 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 ## Answer by Chris Edmonton (score 0) https://quant.stackexchange.com/a/71649 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.
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