OAS and Z-Spreads ??

B

BMiller12

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
If the Z-spread includes the risk associated with the embedded option, why is it not appropriate to use it when valuing a bond with an embedded option ?? You would think that since its spread includes the cost of the option, that it would be better to value a bond with an option.
Correct me if I’m wrong: perhaps the OAS adjusts out the cost of the option in an attempt to draw a more apples to apples comparison with spreads on other noncallable / nonputable bonds. That way when you value the bond, the interest is “cleaner”, for lack of a better term, and now the option impact on value is solely captured by the cash flows (lower CF at a given node if it’s called). Is this to prevent double dipping / offsetting the impact on the bond value that occurs if a z-spread (which includes option cost) and the cash flows (which are also impacted by the option) ? Sort of like the decision to either include country risk in the cash flow or in the discount rate, but not both.
I guess my other general hang up is: how is it that OAS takes into account the option cost when the Z-spread includes the cost of the option (ie higher spread) ?
Thanks for any help and clarification!!
 
Ok here goes. Someone please correct me if I’m wrong.
Both the Z spread and the OAS have the same basic philosophy – to work out the spread that makes the present value of the bond cashflows equal the market price.
The difference is that the Z spread doesn’t take into account the impact that the option might have on the bond cashflows. Eg if the price of a callable bond rises to a certain level, it’s probably going to be called. The Z spread just ignores this probability when it computes the spread.
The OAS, however, does take the potential cashflow changes into account.
Let’s look at a callable bond. Using a Z-spread model, the present value of the cashflows is going to be higher (because the model doesn’t account for the chance of a call). Therefore the spread that’s required to make the PV of the cashflows equal to the market price is higher.
Using an OAS model, the PV of the cashflows is lower (because of incorporating the chance of a call), the market price is the same, so the spread ends up being lower.
The difference between the two numbers represents the option cost.
 
How can the Z-spread not take into account the impact that the option has on the bond if the z-spread includes the option cost (the z-spread is higher than the OAS bc of this cost) ? How does the z-spread ignore it if it includes the option cost in its spread ? Seems like you would use the z-spread to discount a callable bond bc it includes in the interest rate the cost of the option, no ?
 
Furthermore, why is it that in order value the callable bond, the OAS is added to the benchmark..and not the z-spread ? why not the z-spread ? The OAS doesn’t reflect the option so why would you use it. How by adding the OAS are you considering the option characteristics of the callable bond ?
Schweser also says that the cash flows are adjusted for the bond. I get this to the extent you use the lower expected call price. But then it says the option is “removed” by this cash flow adjustment. How is it removed if the cash flows are being adjusted (using $100 as opposed to $101.594) ? Doesn’t this inherently reflect the option since you’re using a lower CF.
 
You are looking at this wrong. Maybe some of the language that Schweser uses is confusing you.
Think about the process of valuing a bond. First you work out all the cash flows over the life of the bond. then you calculate the discount rate, which will make those cash flows equal to the market price. (this discount rate is composed of the benchmark rate, plus a spread.)
the key to all this is remembering that when you are comparing z spread and OAS for identical bonds (apart from one being callable) you are comparing bonds that are trading at the SAME PRICE.
Therefore the difference in spreads is entirely due to the PV of the cash flows. (higher cash flow requires a higher spread to get it to equal the market price).
A callable bond will have a lower cash flow therefore lower OAS compared to the Z spread . A putable bond will have higher cash flows therefore higher OAS.
When Schweser say the OAS removes the option, this isn’t quite correct. It adjusts the cash flows to account for the option.
Try to think of the concept of ‘option cost’ as the cash flows you are giving up because of the option.
the Z spread ignores the option entirely.
Hope that helps.
 
“the key to all this is remembering that when you are comparing z spread and OAS for identical bonds (apart from one being callable) you are comparing bonds that are trading at the SAME PRICE.”
- How are the bonds trading at the same price is one is callable and the other is noncallable, aren’t the cash flows different ? Or are you saying that they are only the same price bc a different (either OAS or z-spread) is applied to the benchmark such that it makes the prices the same ??? I guess i thought the all else equal, the value of a callable bond is/should be less than a noncallable bond due to the embedded option (NC bond-Callable bond = option cost).
Perhaps this is a poor analogy, but is it akin to the decision as how to incorporate country specific risk - either in the cash flows or in the discount rate. That is, if you adjust the cash flows to reflect the country specific risk, then you shouldn’t adjust the discount rate (or vice versa). In that case the discount rate will be less (like the OAS) because the country risk (optionality of the bond) is reflected in the cash flows. Is that at all along the same path of thought??
How can the Z-spread ignore the option if its spread over the benchmark includes the option cost ?
Do you mean it ignores the option bc it’s not being adjusted like OAS in response to the option being in the cash flows?
This stuff is frustrating.
 
Spreads are basically used for comparison that which issue is giving more return with same sort of risks. For comparison it is necessary that issues must be judged on common grounds. Suppose there is an issue giving 135 bps spread and it is option free whereas another issue is giving 145 bps and it has an embedded option in it. If 10 bps is the option cost then both the issues are giving the same spread. If the yield curve is flat then 135 and 145 are nominal spreads and if the yield curve isn’t flat then these are zero volatility spreads. Yes z-spreads do contain the option cost but OAS is calculated after adjusting the cost of option so that the spread to compensate risks other than associated with option is calculated. This is done for comparability. The z spread of an option free bond is compared with the OAS of a bond which has embedded option in it and as the formula goes
OAS = Z spread - Option cost
For option free bond the option cost is 0 so OAS = Z Spread.
I hope it heps.
 
When i said the Z spread ignores the option, I mean that it calculates the cashflows (and therefore the spread) based on the option not even existing. ie in exactly the same way as it would for a non-callable bond. So that’s obviously not the spread you want to use to value a bond with options.
when I was talking about the same price, I was trying to explain why the OAS is lower than the Z spread (because this seems to be one of the concepts that is tripping you up).
Maybe the example would be clearer if you just think about a callable bond. This bond is trading at a set price so all we have to solve for is the spread.
If we use the Z spread to do this, we will end up with a spread that doesn’t reflect any changes to the future cashflows due to the option. Therefore the spread is going to be higher (because the cashflows are higher).
The higher a spread is, the “cheaper” a bond looks in relation to other bonds. So if you look at the Z spread you might be fooled into buying a bond because it looks cheap, but the reason it looks cheap is because the spread is based on a cashflow pattern that isn’t actually accurate.
On the other hand, the OAS adjusts the cashflows for the effect of the option. If the option is a call (which benefits the issuer, not the investor) the cashflows are likely to be lower. Therefore the spread will be lower and the bond will look more “expensive” relative to other bonds. This means an investor can make an accurate assessment of whether they should buy this bond, or choose something else.
To put it another way – the Z spread calculation effectively assumes the investor gets paid the cost of the option (because it’s included in the spread they get). in real life, this isn’t what’s going to happen. the issuer will benefit from the option (assuming it’s a call), not the investor.
hope that helps.
 
Kiakaha wrote:Ok here goes. Someone please correct me if I’m wrong.
Both the Z spread and the OAS have the same basic philosophy – to work out the spread that makes the present value of the bond cashflows equal the market price.
The difference is that the Z spread doesn’t take into account the impact that the option might have on the bond cashflows. Eg if the price of a callable bond rises to a certain level, it’s probably going to be called. The Z spread just ignores this probability when it computes the spread.
The OAS, however, does take the potential cashflow changes into account.
Let’s look at a callable bond. Using a Z-spread model, the present value of the cashflows is going to be higher (because the model doesn’t account for the chance of a call). Therefore the spread that’s required to make the PV of the cashflows equal to the market price is higher.
Using an OAS model, the PV of the cashflows is lower (because of incorporating the chance of a call), the market price is the same, so the spread ends up being lower.
The difference between the two numbers represents the option cost.
Click to expand...
How can the Z-spread not take into account the impact that the option has on the bond if the z-spread includes the option cost (the z-spread is higher than the OAS bc of this cost) ? How does the z-spread ignore it if it includes the option cost in its spread ? Seems like you would use the z-spread to discount a callable bond bc it includes in the interest rate the cost of the option, no ?
Another silly thought, but why can’t you just bootstrap the forward rates to use in the model instead of guessing about volatility and using those rates?
Let me step back, what’s the binomial trying to find? If the rates in the model are simply bringing the value back to equal the price that already exists then what’s the point?
 
you realize that a higher spread is a GOOD thing, right? (Assuming the bonds have equal credit risk etc). It means the investor will be paid more for their investment. So all things equal, you’d prefer a bond with a higher spread over one with a lower spread.
Does that help you understand why the OAS is lower?
as i said in my last post:
the Z spread calculation effectively assumes the investor gets paid the cost of the option (because it’s included in the spread they get). in real life, this isn’t what’s going to happen. the issuer will benefit from the option (assuming it’s a call), not the investor.
 
Kiakaha wrote:When i said the Z spread ignores the option, I mean that it calculates the cashflows (and therefore the spread) based on the option not even existing. ie in exactly the same way as it would for a non-callable bond. So that’s obviously not the spread you want to use to value a bond with options.
Click to expand...
What do you mean by, the Z-spread calculates the cash flows? Are prices for bonds with options the same in the market as though without options (ie assuming they’re otherwise priced correctly)?
when I was talking about the same price, I was trying to explain why the OAS is lower than the Z spread (because this seems to be one of the concepts that is tripping you up).
Maybe the example would be clearer if you just think about a callable bond. This bond is trading at a set price so all we have to solve for is the spread.
Kiakaha wrote:If we use the Z spread to do this, we will end up with a spread that doesn’t reflect any changes to the future cashflows due to the option. Therefore the spread is going to be higher (because the cashflows are higher).
Click to expand...
Why does the z-spread not reflect changes in cash flow. What’s the connection btw the spread and what the actual cash flows are that we are present valuing?
Kiakaha wrote:The higher a spread is, the “cheaper” a bond looks in relation to other bonds. So if you look at the Z spread you might be fooled into buying a bond because it looks cheap, but the reason it looks cheap is because the spread is based on a cashflow pattern that isn’t actually accurate.
Click to expand...
I think i’m following, and i understand the math and how a higher rate effectively results in a lower/cheaper price. Guess i just don’t understand why the cash flows change based on the spread used. I realize that with an option that is called, the cash flows will likely be lower, and therefore you need to use the OAS (lower rate) in order to get back to the same price. Does using a z-spread with higher cash flows not get you to the same mkt price that using a lower spread (OAS) would when applied to lower cash flows? If so, aren’t we just getting to the same answer?
I feel like i generally get it and am getting close, but feel like i’m not connecting a dot somewhere.
 
Kiakaha wrote:When i said the Z spread ignores the option, I mean that it calculates the cashflows (and therefore the spread) based on the option not even existing. ie in exactly the same way as it would for a non-callable bond. So that’s obviously not the spread you want to use to value a bond with options.
Click to expand...
What do you mean by, the Z-spread calculates the cash flows? Are prices for bonds with options the same in the market as though without options (ie assuming they’re otherwise priced correctly)?
Kiakaha wrote:If we use the Z spread to do this, we will end up with a spread that doesn’t reflect any changes to the future cashflows due to the option. Therefore the spread is going to be higher (because the cashflows are higher).
Click to expand...
Why does the z-spread not reflect changes in cash flow. What’s the connection btw the spread and what the actual cash flows are that we are present valuing?
Kiakaha wrote:The higher a spread is, the “cheaper” a bond looks in relation to other bonds. So if you look at the Z spread you might be fooled into buying a bond because it looks cheap, but the reason it looks cheap is because the spread is based on a cashflow pattern that isn’t actually accurate.
Click to expand...
I think i’m following, and i understand the math and how a higher rate effectively results in a lower/cheaper price. Guess i just don’t understand why the cash flows change based on the spread used. I realize that with an option that is called, the cash flows will likely be lower, and therefore you need to use the OAS (lower rate) in order to get back to the same price. Does using a z-spread with higher cash flows not get you to the same mkt price that using a lower spread (OAS) would when applied to lower cash flows? If so, aren’t we just getting to the same answer?
I feel like i generally get it and am getting close, but feel like i’m not connecting a dot somewhere.
 
Ignore the first response with quotes. The one above is cleaner and one you should respond to. Thanks and sorry for double post, it’s late.
 
“Guess i just don’t understand why the cash flows change based on the spread used.”
the cash flows change because of the different assumptions that are used to calculate the Z spread versus the OAS.
In real life, the cashflows you end up getting from the bond obviously don’t change.
But remember, both of these models (Z spread and OAS) are trying to predict what’s going to happen in the future (so you can work out the value of your bond at the present time). They use different methods to do this, so the results you get are different.
The Z spread does NOT consider the possibility that the cashflows will change because of an option. It just assumes the cashflows will occur in the same pattern as on a regular bond, ie as if the option didn’t exist. That’s why it’s not a suitable way to value bonds with options – because it’s not a good forecast as to what the actual cashflows will be.
The OAS model actually considers the impact of the option. Therefore it’s a closer fit with ‘reality’ when you’re trying to value a bond with an option.
“Does using a z-spread with higher cash flows not get you to the same mkt price that using a lower spread (OAS) would when applied to lower cash flows? If so, aren’t we just getting to the same answer?”
to your first sentence - yes! that’s the whole point! but you’re not getting to the “same answer”, you’re arriving at a totally different spread ie compensation to the investor.
Take two bonds. Assume they have identical maturity, credit risk etc.
bond 1: no options. Z spread = 200 basis points, OAS = 200 basis points
Bond 2: callable. Z spread = 200 basis points, OAS = 100 basis points
Which one of these would you rather buy? If you just looked at Z spread, you wouldn’t care which one you bought because they both look to be offering you the same spread. But if you use OAS, Bond 1 is clearly better – it’s giving you twice as much spread for the same credit risk, maturity etc.
hope that helps? I’m running out of ideas on how to explain this so I hope we’re getting somewhere :)
 
Kiakaha wrote:The Z spread does NOT consider the possibility that the cashflows will change because of an option. It just assumes the cashflows will occur in the same pattern as on a regular bond, ie as if the option didn’t exist. That’s why it’s not a suitable way to value bonds with options – because it’s not a good forecast as to what the actual cashflows will be.
Click to expand...
Very, helpful so far. Thank you!
My confusion though with the above quote is that it seems counterintuitive that the Z-spread wouldn’t consider the change in cash flows as a result of the option or as if the option didn’t exist, because the z-spread itself includes a premium for the option ! Am i crazy for finding that a bit confusing ?
A few unrelated questions since you seem to have a really good grasp on this (maybe an email would be better if you don’t mind, if that’s cool?):
1.) To clarify, the bootstrapping process in the prior reading gives us a spot rate treasury curve for which we can either value a treasury bond with – or (now flowing into this reading) use the same spot rate curve but add some additional spread (ie z-spread or OAS) to value non-treasury bonds, correct?
2.)There’s no way to just bootstrap the necessary rates to value a bond with options is there, instead of using a binomial tree ? Is bootstrapping really just for determining treasury spot rates ? Why does the bootsrapping process not incorporate volatility like the binomial model - I guess maybe we start with the bootstrapped model to find the spot rate curve which we then incorporate those rates (plus a spread if necessary) in the binomial model. Bc the model incoporates volatility, the spot rates from the treasury curve ARE being impacted by volatility bc the rates/yields in the model are based in part on treasury spot rates, no? Maybe i didn’t word that well.
3.) I guess i used to think that we would value a bond using YTM to find the new price, and thus determine the premium or discount it’s currently trading at. Is YTM not how you should value a bond, should we not be using a spot rate curve instead? Just missing the connection bc on Level I it seems that’s what we used most when valuing/determining price of bonds. When do you use YTM vs spot rate curve (maybe the spot rate curve is more theoretical and not used in practive whereas YTM is…(shoulder shrug)?
4.) If the idea of spot rates apply and it is therefore best to use different rates at for different CF at diff points in time, is this not true for valuing equity securities too say using a DCF ?? why do we only use one discount rate/WACC when discounting all future cash flows ??
5.) Sort of a separate question but going back to spot rates. What makes a spot rate on a zero coupon bond yield so much better / “cleaner” (for lack of better terms and understanding) for determining a spot rate curve, and therefore better for pricing ?? Is 5-yr corp bond issued today not a spot rate ? Why can one just use the YTM at different maturities to value a bond ? This overcomes using a single YTM to value all the cash flows, right? So why do we need a spot rate curve.
6.) Lastly, are forward rates simply implied rates…that is, are they not actual real rates in the marketplace ?
Thanks a ton if you have the time to help with this. I’d really appreciate it because obviously I need it!!!
 
BMiller12 wrote:My confusion though with the above quote is that it seems counterintuitive that the Z-spread wouldn’t consider the change in cash flows as a result of the option or as if the option didn’t exist, because the z-spread itself includes a premium for the option ! Am i crazy for finding that a bit confusing?
Click to expand...
no you’re not crazy for finding it confusing. You’re just looking at it wrong. You get that a call option has value for the issuer, not the investor, right? And that (all else being equal) investors prefer a higher spread? If you put these two concepts together it seems pretty intuitive that the existence of a call option would LOWER the spread (ie the bond would be less attractive to investors).
To rephrase: the spread represents the compensation (over a benchmark rate) that investors will receive for buying a bond. The model that you use to calculate a Z spread doesn’t have the capacity to work out cash flow changes resulting from an option, therefore it will calculate a higher compensation (ie spread) than what’s actually likely to occur.
When the textbooks say ‘option cost’ try to think about it as the cost to the INVESTOR ie, the extra spread they are giving up as a result of the option. When they say the Z-spread “includes the option cost”, they mean that its calculation assumes that investors get to keep that extra spread (ie they will receive the same spread as if the option didn’t exist). This isn’t actually what’s likely to happen in real life.
To your other questions:
1) Yep, that’s correct
2) Not entirely sure what you mean here. But in general, bootstrapping and the binomial model follow the same principle: you’re assuming that arbitrage doesn’t exist, and therefore deriving rates that equate the cashflow streams to the market price.
3) The YTM is the yield you will get on your bond if you hold it to maturity, assuming you can re-invest the coupons at the same YTM. A spot-rate curve is just the YTMs on zero-coupon bonds of different maturities (ie removing the uncertainty around whether you can re-invest the coupons at the same YTM). More generally – most bond funds are trying to outperform a benchmark, rather than achieve a certain yield level. That’s why spread is more important to them (because it measures your compensation over and above a benchmark). Whether they use a nominal spread (ie a spread based on the YTM) or a Z-spread will probably depend on the sophistication of the investor. You can use either, but there are drawbacks to the nominal spread (as covered in the textbook).
4) No idea. Maybe more complicated equity models do incorporate different discount rates? I would guess though, that there’s more certainty with bond cashflows - unless options are involved, you know exactly how much $ you’re getting at different points in time. With equity valuations, the dividends and the terminal value are uncertain so there’s a lot of guesswork in there anyway. So maybe it’s less important to get the discount rate exact.
5) Have kinda answered this above: The YTM on a coupon bond is the yield you will get on your bond if you hold it to maturity, ASSUMING you can re-invest the coupons at the same YTM. This is a big assumption to make and it might not actually be possible. Therefore the yield on a coupon bond may not be an unbiased forecast of future interest rates, because it includes this uncertainty.
Using a bunch of YTMs to value all the cashflows wouldn’t solve this problem. The solution is to use zero-coupon bonds, ie spot rates. This produces an ‘unbiased’ curve that’s just based on interest rate expectations, not other factors.
6) No idea what you mean by this, sorry.
 
So why invest in bonds with call options…only if the investor was receiving a higher yield/coupon? For instance, say the option-free bond has a 6.5% coupon, the investor would/should only invest in an otherwise comparable yet callable bond if the coupon was say 7.0% (assuming the option cost is 50 bps or less). Otherwise they’d be earning more on the option-free bond?
So after adding/subtracting the OAS to get the Model price to equal the Mkt Price, the Pos/negative amount is compared to what…an option free bond? Or a comparable callable bond?
Thanks again, Aaron. I’m trying
 
More confusing bc every bond in the book (callable and noncallable) has the same coupon (6.5%). I would think that the callable bond should have a higher yield bc isn’t it obvious at that point that the return on the callable bond is less than the noncallable bond?
 
You must log in or register to reply here.
Back
Top