# How can OAS be negative?

I have been remembring level 1 notes and what comes to my mind is that OAS for putable bonds is greater than Z-spread because option cost is negative, so how can OAS be negative? My tutor told me that it can be possible only in case of putable bonds but I couldn’t digest the whole thing.

can somebody help?

Option Cost = Z Spread - OAS

Assume you’re the investor. The Z Spread is the minimum rate of return you want to earn. However, it doesn’t account for options. If the bond had a call option (an MBS, for e.g.), you have sold an option to the borrower. That is, the borrower has an advantage over you… so your out of pocket cost has to be lower. So OAS is negative, meaning option cost is positive.

In case of a put option, you have an advantage over the borrower. So your out of pocket has to be higher. So OAS is positive, meaning option cost is negative.

They way you described, if OAS were negative, the market value of callable bond would have been quite high, which is not the case because we know that callable bond value does not exceed straight bond value. Right?

Value of a callable bond = Value of an option-free bond - Call option/Option cost

Positive option cost (to you) decreases the price of a callable bond (negative convexity).

Value of a putable bond = Value of an option-free bond + Put option/Option cost

Negative option cost (to you) - think about this: cost can never be negative! A negative cost to you means money in your pocket. Not the best way to describe, but I can’t think of a better e.g. So the price you pay is higher. So when we think of a negative option cost, it’s means we’re going to have to pay more. I guess you have to apply some boolean logic here, but hope it makes sense.

Maybe someone else can help explain it better.

thanks…