The price of the callable bond needs to be lower than option free bond as the investor has a disadvantage. So, he gets “compensated”.
I know OAS = Z-spread - option cost, and for callable OAS < z-spread
But, shouldn´t the investor also be compensated by receiving a higher OAS than an option-free bond? This IS however an advantage of the issuer, as previously said…
Many thanks!
I think you are not getting the point right. How about making the _ Option Cost Negative _ here. That should take away the confusion. As you may remember the Call Option in a callable bond accrues to the Issuer and the put Option in a putable bond to the Holder. Hence for the call option, the issuer must pay the premium to the Holder ( which becomes a negative cost) and vice versa for a putable bond.
Please do not mug the mindless formula. At L3, you ought to assimilate better 
The investor is being compensated with a higher yield, because the issuer is benefiting. Convexity costs money and the issuer is paying for it.
This yield is not the OAS. The OA(djusted)S adjusts this yield to negate the effect of the option, making it lower than the z-spread. It takes out the yield that the investor was getting for forfeiting convexity (selling a call on the bond).
The opposite is true for a putable bond.
Yes, of course, nowit is clear… you take the perspective of adjusting the spread, i.e. removing the option effect.
The issuer pays you the price in a callable bond, so the OAS is what you have received, absent the option.
Thankyou, guys!