How Zero Curves Are Bootstrapped from Coupon Bond Prices
Summary
The document asks whether using coupon-bearing bonds to derive zero-coupon rates is circular when those rates are then used to value coupon bonds. The answer explains that markets often lack traded zero-coupon instruments, especially at longer maturities, so practitioners infer a zero curve from available bonds. The resulting curve supports arbitrage-consistent valuation of derivatives and can also be used to price new or less liquid bonds against a set of liquid issues.
A second response distinguishes a bond’s stated accretion path from its market yield. For a discounted bond that accretes toward par, the contractual rate provides a path to maturity value, while the market price and yield can move around it. Credit impairment or poor liquidity can cause meaningful premiums or deviations. The discussion is qualitative and does not give a bootstrapping algorithm, worked example, or specific curve-fitting method.
Key ideas
- Market zero-coupon rates can be inferred from coupon-bearing bond prices when zero-coupon instruments are unavailable.
- A constructed zero curve is used to value derivatives and less liquid bonds.
- The bond’s contractual accretion rate and its market yield are distinct quantities.
- Credit deterioration and illiquidity can widen the difference between market pricing and the contractual accretion path.
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Full text
# Basic question about bonds pricing # Basic question about bonds pricing I decided to recap my knowledge in interest rates, and decided to start with Chapter 4 on interest rates (in 8th edition) of the Hull's book "Options, Futures and Other derivatives". In 4.3 the concept of a zero-coupon rate is briefly introduced, and is further used to price a coupon-bearing bond in 4.4. Procedure is natural, logical and relies on clear arbitrage-avoiding arguments. However, in 4.5 zero-coupon rates are themselves computed via the coupon-bearing bond prices. This line feels cyclic to me. I can understand that one can use this to check the consistency of bond prices over several maturities, but does it mean that one can actually price bonds using such arguments? ## Answer by Brian B (score 5, accepted) https://quant.stackexchange.com/a/9014 Generally, there are few or no zero-coupon instruments traded in the market, especially for longer maturities. However, pricing of many derivatives relies on having a zero curve, so it becomes necessary to construct one using available instruments. Aside from derivatives, one can use a zero curve fitted to liquid bonds to price new or less liquid issues. ## Answer by jessica (score 2) https://quant.stackexchange.com/a/9016 Yea, I just started work at a fixed income shop. We accrete the value of zero coupon bonds based on the coupon rate the bond would have paid if it were an interest/bullet bond. The value of the coupon/accreted rate in the Official statement/indenture of the bond is obviously not the rate the market is pricing the bonds at but it fluctuates around it, assuming the obligor's credit worthiness is not impaired and there is liquidty in the market, otherwise you would have large credit, liquidity premiums. Just think of the accretated rate as a glide path that gets you from the value of the bond now to the par amount at maturity and that the market price/yield, which is different, will fluctuate around this accreted rate all the way up to par.
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