# OAS vs Z-spread

Z-spread = OAS + Option cost

option-free bond used z spread while option embeded option uses OAS. so confused that bond with embeded option must be riskier than option free bond, why use OAS which is smaller than Z-spread . My point is that the riskier bond should have higher spread to compensate for it

there’s too much confusion in that sentence to comment on. i’d recommend going back to the reading - it will bring some clarity.

I think you got some of the ideas mixed up but you are spot on on the concept that higher risk requires higher spread to compensate for the added risk taken. But it is not really applicable on this equation.

When we say Z = OAS + Option Cost, we are not refering to Z spread from a option free bond vs the OAS from another bond with optionionality. The idea is simply that for an option free bond, the Z spread and its OAS is the same because there is no optionality (and option cost is zero). But for a bond with embedded option, the Z spread is higher than it’s OAS because Z spread reflects credit, liquidity and option risk. But OAS is already adjusted for option cost or you can treat it as option removed spread.

Thus, when we compare bond without embedded option with Z spread of 350 bps against a callable bond with embedded option with Z spread of 500 bps and OAS of 300 bps with the same duration, we use the OAS of 300 bps to compare against the option free bond 350 bps spread and not the Z spread of 500 bps. This allows us to make a more meaningful apple to apple comparison because we have already removed option risk from the callable bond by using OAS to compare against a option less bond’s Z spread (which is also same as it’s OAS).

Hope this clarifies your undestanding

OAS = Option free/removed spread that considers only credit and liquidity risk.

g3r41d- that did help but one thing i dont understand is how the OAS is the average spread over the life of the bond, because the OAS is only used on the spot curve not the yeild curuve correct? understanding this part of fixed income has been my biggest down fall So you can only compare option free and callable bonds that have same maturity?

Thanks. So confused. For Monte carlo method , each node has to add OAS to compensate for the optionality. while OAS already dedcucted the Optionality and leaves only (liquidity +credit risk). if they value the bond with option , they should keep the optionlity in the spead to compensate for the risk, why use OAS ( without the otptionlity).

I think that’s where most people initially get confused. Why OAS without option risk is used to value bond with options. The idea of using OAS is really to find the spread of the bond against a reference benchmark without the option cost. Because of its embedded optionality, the value at each node in the binomial tree is not necessarily equal to its discounted present value of it’s one period ahead value. The OAS is the spread that is added to every single spot rate to make the value of the bond at t = 0 similar to the market value.

With this, we will have eliminated the option cost and we can use the OAS to compare against other similar option free bond or similar callable or putable bond.

^As he said - key is to remember that the OAS is just used for comparison purposes (and when developing a tree to use to find effective duration and maturity). The actual pricing of the bond is still done using the rates that are assumed by the binomial tree model.

g3r41d, so if you compute the OAS on an already option-free bond, you’ll get the Z spread, correct? If the bond is callable, its market price is lower than a non callable bond, b/c it has some strings attached, i.e., the issuer can take it away from you. So, a callable bond will have an OAS which is larger than a non callable bond…? If puttable, then OAS is smaller?

Your second statement is confusing option cost with OAS. A callable bond won’t have a larger OAS… it will have an option cost.

Although it typically wouldn’t be thought of as subtracting the cost of the option… you would calculate the OAS and then compare that to a similar option-free bond, and then basically say the difference is the cost of the option.

In a hierarchy, Nominal spread - Option Cost - OAS = 0.

If a bond doesn’t have an option, then Nominal Spread technically = OAS.

Yes for option free bond, Z spread = OAS since option cost is 0 as it is option less.

I think it’s better that you think of option cost here as the additional spread to take on added (call) option risk compared to an otherwise option less bond. And for putable bonds, the option cost is negative because it is a benefit.

OAS will not be larger or smaller for non callable or putable bond. In fact if a callable and putable bond is similar in maturity, credit rating, duration, etc, its OAS is the same.

To make things simple, just think of OAS as option removed spread, so you can use this to compare against other similar bonds or benchmarks. Note that a bond high OAS relative to it’s option cost is a better investment than one with a low OAS relative to high option cost.

" The OAS is the spread that is added to every single spot rate to make the value of the bond at t = 0 similar to the market value

So the Value of the Bond after the discount which is equal the market value. is this bond price still embeded option or option free?

Thanks

Since it is market value, the bond with or without option is already priced by the market. You need to know that regardless of using Z spread or OAS, the intended outcome is to make the discounted value = market value.

Quiz1: You set up a binomial tree based on treasury spot rates to value some bonds. If you find that the OAS of a AAA corporate bond is 70 bps, is the bond undervalued/overvalued? Explain.

Quiz2: Using the same tree, you find that the OAS of a AA corporate bond = -10 bps, is the bond undervalued/overvalued? Explain.

Q1 could be over or undervalue. Triple a == riskiness since company can’t print money. Also there is liquidity risk. You not sure if the credit risk plus liquidity is risk is worth more or less than 70 bp.

Q2. Over value. Ur earning less than the spot rate. It means that credit risk and liquidity risk is negative, which is impossible. It’s better if you just purchase a treasury bond

Q1 could be over or undervalue. Triple a == riskiness since company can’t print money. Also there is liquidity risk. You not sure if the credit risk plus liquidity is risk is worth more or less than 70 bp.

Q2. Over value. Ur earning less than the spot rate. It means that credit risk and liquidity risk is negative, which is impossible. It’s better if you just purchase a treasury bond

That’s it.