Bootstrapping Spot Discount Factors from Par Bond Yields

Summary

The document considers how to derive a spot yield curve from par coupon rates across bonds with different maturities. It presents a sequential discount-factor calculation: first obtain the one-year discount factor from the one-year par coupon, then use that known factor with the two-year par coupon to solve for the two-year discount factor. The stated formulas assume a face value of 100 and use the coupon rate for each maturity.

This is an outline of the bootstrapping idea: use shorter-maturity discount factors to isolate the value of later cash flows. The text gives formulas for the first two maturities but does not continue the procedure to later years or discuss coupon payment frequency, day-count conventions, compounding, or market-data requirements. Its scope is therefore a basic setup rather than a complete curve-construction specification.

Key ideas

• Spot discount factors can be derived sequentially from par coupon rates.
• The one-year bond provides the initial discount factor.
• The two-year discount factor is solved using the known one-year factor and the two-year par coupon.
• The formulas use a face value of 100.
• The document does not specify conventions needed for a complete curve construction.

Tags

# Retrieve SYC from Par yields


# 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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.