Z-Spread: Definition and Calculation

The problem with nominal spread is that it measures the spread at just one point on the yield curve. The z-spread solves this problem by considering the spot yield curve instead of the standard yield curve.

The z-spread, also known as the zero-volatility spread or the static spread, measures the spread that the investor will receive over the entire Treasury spot rate curve.

For the purpose of calculation, we start with an assumption for the z-spread. One takes the Treasury spot rates for each maturity, adds the z-spread to it, and uses this new rate as a discount rate for each maturity to price the bond. The correct z-spread is the one that makes the present value of cash flows equal to the price of the bond.

$P = \frac{C_1}{(1+r_1+z)} + \frac{C_2}{(1+r_2+z)^2} + \frac{C_3}{(1+r_3+z)^3} + \cdots + \frac{T}{(1+r_n+z)^n}$