seems poorly worded, perhaps the part, “to the price of an otherwise identical option-free bond.” is part that is least accurate. where did this question come from? if it was on the exam, i would be pissed, because it serves only to be tricky with wording and not test the facts.

To be true, c would need to read: The zero volatility spread is the constant spread that is added to each Treasury spot rate to equate the present value of a bond’s cash flows to the market price of the bond.

Wait a minute - that’s what the answer says. The answer is correct and is different from the wording in the question.

I agree that the original wording of c may be quite clumsy, but it is actually theoretically correct, and explicitly clear. There is no Z-spread for an option-embedded bond. When one talks about Z-spread for an option-embedded bond, it implicitly means the z-spread for an identical bond with the option stripped out (thus matching the market price of this identical option-free bond, not the market price of the option-embedded bond)

Nope. The z-spread is a really simple calculation where you take Market price of bond = coupon1/(1 + r + z-spread)^t1 + … + couponk/(1 + r + z-spread)^tk + principal/(1 + r + z-spread)^tk The market price of a bond with an embedded option is different from a bond without an embedded option. Where you are getting messed up is that the z-spread is the spread over treasuries assuming that the bond is held to maturity. A high z-spread can be due to optionality, credit unworthiness, liquidity, taxation, etc…