# Retrieve SYC from Par yields

Currently studying about fixed income and the construction of the Spot yield curve, but I do not know whether my intuition is right.

Suppose we have a firm that has traded Bond for different maturities (1,2,..,T). The Par yield of each Bond equals it's yield to maturity. Given the par coupon rates, we can construct the Spot yield curve. For the bond with maturity of 1 year, we discount to get the 1 year discount factor $$d(0,1)$$

$$d(0,1)=\frac{100}{C(1)+100}$$

Since, we know the d(0,1), for the 2 year discount factor

$$d(0,2)=\frac{100-C(2)* d(0,1)}{C(2)+100}$$

Where $$C(i)$$ the Par coupon of the bond with maturity i years

• If your question is whether the above procedure is correct for bootstrapping the zero curve from the par curve then the answer is yes. In practice though you would not have par bonds for each whole maturity but only for key maturities such as 1,2,3,5,7,10, etc. Then it becomes more interesting how to construct the zero curve. – Frido Rolloos Jun 8 '19 at 15:57