# Why is OAS larger than Z-spread for PUts?

Why is OAS larger than Z-spread for PUts? I keep fumbling with the logic. OASZ-spread? why? The bond has a higher yield without the option? With the option i have to take a lower yield since it benefits me?

Letâ€™s say you require a 5% yield. If you take an option free bond with a 5% coupon, it will sell at par. If the same bond is callable, itâ€™s going to sell at a discount, right? So therefore, itâ€™s YTM is going to be higher than 5% - at least as long as you donâ€™t take into account the option. If you take into account the option, the cash flows are lower (at least in some scenarios) and the yield over the interest tree, taking into account the option (OAS), will probably be around 5%. If the bond is putable, itâ€™s going to sell at a premium, so the YTM is lower than 5% - again, only based on the nominal coupon rate. Not accounted for the option yet. If you account for the put option, the cash flows in some scenarios are higher than for the option free bond. If you look at an interest rate tree, there might be some nodes where the option free bondâ€™s PV is below 100. For the same node, the putable bond will be put, and you cash in 100. So the cash flows are higher. This means the yield (OAS) is going to be higher than YTM based on the coupon rate. Probably around 5% (or I should be doing some FI arbitrage instead of sitting here and writing this). Hope that helps.

OAS = Z-spread - option cost A put option has value to the bondholder. So the value is positive. If option cost in the above equation is positive, then OAS>Z A call option has value to the bond issuer. Value is negative to the bondholder. If option cost in the above equation is negative, then OAS

Shorter version: When computing the OAS of a putable bond, you are looking at higher cash flows, so you end up with a higher yield than when computing Z spread.

But topher, according to your formula: If Z spread is 5%, and option cost is 1% (positive for a putable bond), then the OAS is 4%. So, OAS < Z spread. Shouldnâ€™t the formula be: OAS = Z-spread + option cost???

Sorry my post should have read: OAS = Z-spread - option cost A put option has value to the bondholder. So the option cost is negative (you must pay for the option). If option cost in the above equation is negative, then OAS>Z A call option has value to the bond issuer. The option cost is positive (issuer must pay you for the option). If option cost in the above equation is positive, then OAS But topher, according to your formula: If Z spread > is 5%, and option cost is 1% (positive for a > putable bond), then the OAS is 4%. So, OAS < Z > spread. > > Shouldnâ€™t the formula be: OAS = Z-spread + option > cost???

OAS = Z-spread - option cost The formula is from whose perspective? Bond issuer or bond buyer? S

From the buyerâ€™s POV. â€śoption costâ€ť is negative if you pay, and positive if you receive something. So for the putable bond, OAS > Z-spread.

Sorry guys, i am completly mess up with this point.
I read a question which sais: Callable debt has a smaller option- adjusted spread than comparable non- callable debt.

As far as i know: OAS>Z => Putable // OAS<Z=> Callable. So, this statement should be right and is not. Why?
Looking forward your help.

The OAS on a callable bond should be the same as the OAS on an otherwise identical non-callable bond.

OAS removes the value (i.e., the spread) of the call option.

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