OAS, Z-spread and volatility

Do OAS and Z-spread depend on interes rate volatility?

For example assume that we have bond with embedded call option and OAS + opt cost = Z-spred. Now volatity goes up and so does option cost. Now, will OAS go down or Z-spread go up to keep the equation still valid?

Or am I missing something obvious along the way…

Because the “Z” is Z-spread means “zero-volatility”, changing the interest-rate volatility should have no effect on the Z-spread; thus, if the option value changes when the volatility changes, the OAS should change by the same amount (in the same direction for a option owned by the bondholder, and in the opposite direction for an option owned by the issuer).

The way i understand it, OAS is the spread between the Value of a Security with an Option and the value of a security with no option.

Since a call option is negative to the holder of a security with embedded call, the value of a security with call options should decrease with an increase in interest rate volatility, which will in turn make the OAS to drop.

The Z spread will stay constant.

Thanks guys, Z-spread is indeed constant so OAS has to change. However I don’t quite understand why…

I thought it is the other way round.

Should’t it be the OPTION COST which is the spread between the Value of a Security with an Option and the value of a security with no option?

Yes, option cost = value of the bond with option - value of the option free bond

OAS is the spread of the bond with option when you take out the option cost or OAS=Z-spread - option cost, which brings us to the magician’s point that OAS moves in the same direction as bondholders option (put option) and in the opposite direction for the bondissuer’s option (call option). This relation can be observed through the previous formula OAS = Z-spread - option cost, so if you have a put option it’s cost is negative, and than you get the formula OAS = Z-spread - (-put option cost) or OAS = Z-spread + put option cost so you see the same direction of movement of put option cost and OAS. If you have a call option it’s option cost is postive and you have OAS= Z-spread - call option cost and the inverse relationship between OAS and call option cost.

Value of a put option goes up, OAS goes up.

Value of a call option goes up, OAS goes down.

I think that that’s how it works.

I suspected that put option cost is negative and call option cost is positve and that is where all the problem stems from.

Thank you guys, it’s good you’re there!

wait, what, hold on a second. I thought it was the other way around.

I thought that OAS was the “option adjusted spread”, therefore removed the cost of the option from the equation, which allows you to look at the bond based on other factor (i.e. credit risk, liquity risk, etc). So if you had 2 bonds, one that is callable and one that is not from the same issueer, in theory, their OAS should be the same if they are both trading in line with the market (i.e. the market is pricing the same spread for credit risk, etc).

My understanding of the Z-spread was that it could be all over the place for different bonds, which is why it is not a good measure to compare a bond with an option to a bond without an option. The z-spread on a callable bond should in theory be higher than the z-spread on a a bond with no option from the same issuer.

My undestanding is that as the option cost moves (due to say interest rate vol moving, holding everything else constant), the option cost would change, the OAS would remain the same, and the Z-spread would move in line with the option cost move.

Have I got this topic so wrong?

so is it safe to say OAS moves in relationtion to the interest rate? rates go up > put option value goes up > OAS goes up?

Schweser FI Book, p196.

"The Z-Spread is the spread taht when added to each spot rate on the yield curve, makes the present value of the bond’s cash flows equal to the bonds’s market price. Therefore, it is a spead over the entire spot rate curve. The term zero volatility in the z-spread refers to the fact that it assumes interest rate volatility is zero. If interest rates are volatile, the z-spread is not appopriate to use to value bonds with embedded options because the z-spread includes the cost of the embedded option. " My takeaway from this is that option cost directly affect the z-spread, as option costs move, so does the z-spread.

“The OAS is the spread on a bond with an embedded option after the embedded option cost has been removed.” My takeaway from this is that the option cost doesn’t affect the OAS. You’re stripping out any effect of the option. You can compare bonds from the same issuer with different options or no option at all on a like for like basis. The OAS has nothing to do with the option.

“OAS = Z-spread - option cost” This makes is sound like OAS is dependent on the option cost but my interpretation of this formula goes more like this “Z-Spread = OAS + option cost” Same thing but it’s the z-spread that’s affected by the option cost (i.e. OAS is the constant with changing option cost, and it affects z-spread).

my understanding of the Z in z-spread is that it means that you NEED to assume zero volatility for this measure to be worth anything. If option are included in your bond and vol<>0, you should not be using a z-spread.

You’re correct. I think the misunderstanding arises from the assumptions we’re making here.

If the value of, say, a put option rises, and the Z-spread doesn’t change, then the OAS will increase. Note that by stating that the Z-spread doesn’t change, we’re saying that the price of the bond doesn’t change. Perhaps (probably) that’s an unreasonable assumption, but that’s the one that started this whole discussion. In reality, the price of the bond will increase, the Z-spread will decrease, and the OAS will remain (nearly) unchanged.

If the value of a call option rises, and the Z-spread doesn’t change, then the OAS will decrease. Again, we’re assuming that the value of the call option increases, but the price of the bond doesn’t change. In reality, the price of the bond will decrease, the Z-spread will increase, and the OAS will remain (nearly) unchanged.

So with any change in value of the option (due to change in volitility) OAS will remain unchange because there is no option risk involved? but as both nominal and z spread have an option risk change in value of the option will effect both?


OAS= NOMINAL- Option cost

Now when interest rate rise then value of put option increases as investor may prefer selling bond when price falls

When interest rate fall call option becomes more valuable for issuer

Case 1- When interest rise , Call option value increase so OAS reduces, Z spread= OAS+ Call option value

Case 2- In case of put option OAS=Z spread.+ Put option value

Discalimer : my own understanding

If an investor is funded investor then how to see if bond is undervalued according to OAS ?

Pg no 338 first paragraph

"The terms “rich,” “cheap,” and “fairly priced” are only relative to the benchmark. If an investor is a funded investor who is assessing a security relative to his or her borrowing costs, then a different set of rules exists. For example, suppose that the bond sector used as the benchmark is the LIBOR spot rate curve. Also assume that the funding cost for the investor is a spread of 40 basis points over LIBOR. Then the decision to invest in the security depends on whether the OAS exceeds the 40 basis point spread by a sufficient amount to compensate for the credit risk.".

To Vicky: read page 337.

When OAS > benchmark OAS => cheap => buy

When OAS< benchmark OAS => rich=> sell

I need to mark here as well.