Here are my thoughts on the topic. Hopefully, this won’t confuse you further. Also, I tried to decipher your chart, but it has TMI, so I didn’t bother to analyze it further.
OAS accounts for the value of the option. It may be useful to imagine the formulas of callable bonds, putable bonds, and options when thinking about OAS:
P(CB) = P(NCB) - P(Option)
P(PB) = P(NPB) + P(Option)
where:
CB = Callable Bond
PB = Putable Bond
NCB = Non Callable Bond
NPB = Non Putable Bond
Notice that P(Option) can be represented as:
P(Embedded Option in Basis Points) = Z-Spread - OAS
Thus, OAS = Z-Spread - P(Embedded Option in Basis Points)
From an investor’s standpoint, for the callable bond, the option cost is POSITIVE. The option cost (to the investor) is POSITIVE because the issuer has the option to call the bond. Based on the above formula, the OAS of the callable bond will be lower because you’re subtracting the POSITIVE cost. Ultimately, the OAS will be lower than the Z-spread, and by association, lower than the nominal spread.
From an investor’s standpoint, for the putable bond, the option cost is NEGATIVE. The option cost (to the investor) is NEGATIVE because the bondholder has an advantage over the issuer. Based on the above formula, the OAS of the putable bond will be higher because you’re subtracting the NEGATIVE cost (thereby ADDING to the Z-Spread). Ultimately, the OAS will be higher than the Z-spread, and by association, higher than the nominal spread.
I typed this up hastily, so if someone sees an error/typo, please point out.
Hope this helps.