# 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!

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.

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

• I mean no disrespect; fixed income terminology is incredibly (and IMO unnecessarily) complex, but what books/reference material are you using to learn about yield curve modeling? I went through all the answers you posted today and nearly all of them have some conceptual issues. In this case, unless all the bonds happen to be par bonds, the resulting curve won't be a par yield curve. The answer provided Richi is correct. Par yields (also called par coupon rates) are theoretical yields/coupon rates for bonds trading at par. Feb 16, 2022 at 5:08
• I appreciate your thoroughness Helin and strongly agree that bonds and bond markets are made to sound unnecessarily complex. As an institutional fixed income portfolio manager it has been made clear to me that there is a significant disconnect between the academic prescription and practical implication in trading and portfolio management. I think that if things are explained in a manner that is tied to real world implications then people can get a much better and more nuanced understanding of bond market mechanics. Instead of a trying to force an equation/definition based understanding.
– JPI
Feb 20, 2022 at 22:43
• I see that you go to a great deal of trouble to try and help people understand the topic of bond markets. I encourage and applaud your efforts. All the best.
– JPI
Feb 20, 2022 at 22:44