Constructing a Par-Yield Curve from Bond Prices
Summary
The document explains the par-yield curve as a plot of bond yields to maturity against their terms to maturity. A par yield is the coupon rate that would make a bond’s price equal to par; for a bond priced at par, its coupon rate and yield to maturity coincide. The answers describe calculating each bond’s yield to maturity from its observed market price and plotting those yields by maturity.
The discussion distinguishes this curve from a zero-coupon curve: the latter can be derived from par yields by bootstrapping. It does not provide a detailed derivation, worked example, or treatment of practical curve-building choices such as coupon schedules, interpolation, or instrument selection. The guidance is therefore a conceptual starting point, and its direct plotting description assumes the available bonds are suitable for representing the maturities of interest.
Key ideas
- A par yield is the coupon rate that prices a bond at par.
- The par-yield curve plots bond yields to maturity against their terms to maturity.
- Observed bond prices can be used to calculate yields to maturity for the curve.
- A zero-coupon curve can be bootstrapped from par yields.
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# Deriving the par-yield curve # Deriving the par-yield curve Given for example 6 bond prices and their respective 6 cashflows over a time period of 6 years, I have managed to derive the zero-coupon yield curve using the bootstrap method. However, it got lost on me when it came to deriving the par-yield curve. Any help on this? Thank you! ## Answer by Richi Wa (score 1) https://quant.stackexchange.com/a/9234 If you look at wikipedia then you find the definition that a par-yield is the coupon rate, such that bond prices are $100$. This is the definition. Consider $N$ bond with a given coupon rates $c_i$, times to maturity $T_i$ prices $P_i$,for $i=1,\ldots,N$. Then you can calculated the yield-to-maturity for each bond $y_i$. Some mathematics reveal that a bond with coupon rate equal to its yield-to-maturity is priced at par (its price is $100$). Thus the par-yield curve is a plot of the time-to-maturity and the yield-to-maturity of your bonds. As a next step you could derive a zero-rate curve from it by bootstrapping. ## Answer by JPI (score 0) https://quant.stackexchange.com/a/69879 The par yield curve is the curve made up from calculating the yield to maturity of each bond and plotting it against the term to maturity. So this is taken directly from market prices. We then take this curve and derive the zero-coupon curve through the method I explained here: Construct zero coupon curve from current market yield curve
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