How Bond Moneyness Affects Z-Spread and I-Spread Comparisons

# Z-Spread vs I-Spread for Govies - Does moneyness have an effect?


# Z-Spread vs I-Spread for Govies - Does moneyness have an effect?












When calculating the z-spread of a government bond; we find matched zero rates for coupons and maturity, and then calculate the yield by adding/subtracting a spread and then calculate with present value of discounted coupons with for instance OIS.

But when we calculate spread directly vs swap curve (OIS curve in this example), can it be meaningfully different from z-spread for bonds which are trading deeply at discount or at premium? For instance, consider a g-bond with clean price 50. Does the z-spread vs I-spread (swap curve is identical for both) diverge?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/82263

Please recall that the I-spread of a bond B off of a yield curve C is the difference between B's yield and the yields of the two nearest bonds on C linearly interpolated to B's maturity. I-spread provides a quick indicator of the extra yield that B pays in comparison with C. I-spread is easier to compute "manually" than e.g. Z-spread, in which you discount cash flows. But what does I-spread mean when B is on the same yield curve - e.g. B is a government bond and C is the same government yield curve? There may actually be small differences e.g. between on the run / off the run bond yields, or bonds paying very different coupons for historical reasons but trading at similar yields, but the noise from the simplistic calculation (linear interpolation?) will drown them out, so I-spread isn't a very meaningful way to look for these differences.

A bond price of 50 cents, or 200 cents on a dollar could arise in many ways. As a crude numeric example, price 200 might happen the bond is paying 15% coupon and was issued at par some years ago when 15% were the yields, but now the yields are closer to 1%, so the bond has to trade in secondary markets this much above par in order for its yield to be close to the yields of similar bonds being issued now at par. Conversely, a zero-coupon bond maturing in 5 years (the U.S. treasury doesn't issue such bonds, but many others do), priced at 50, yields "only" ~15% a year, which is pretty reasonable for many currencies.

When you calculate a Z-spread off of a swap curve, you actually discount bond's every cash flow using the (shifted) swap curve. So depending on the shape of the curve, you might be discounting some intermediate coupon payments by something very different from the government yield that you use for I-spread. I suggest that you try computing Z-spreads using not just the observable swap curves, but various shapes of the swap curve, starting with flat curve; and various bond coupon schedules, including zero coupon, and, conversely, a large amortization early in its life.