OAS

CFA Level II Fixed Income
#21

Do you know what the _ Z _ in Z-spread abbreviates?

#22

oh my word…

Zero volatility

#23

I think there is a “real” or actual OAS which is derived from the market prices, because OAS is a calculated spread (not a real one like the Z), which we add to all interest rates in the binomial tree in order to force the calculated value to be equal to market value.

If we modify the level of volatility, we will need to modify the OAS as well or the calculated value of our embedded bond will be erroneously higher or lower than the market price.

So I think if we are doing some sensitivity analysis and modify our level of IR volatility we will have to change the OAS for the embedded bonds. But for a straight bond we will not test sensitivity to volatility because it doesn’t affect straight bond value.

So in this case the OAS of straight and embedded bonds will differ, but only in our hypothetical scenario and not in real life.

#24

I thought the Z stood for “Zero clue what’s going on”.

So to summarize the current stage of this discussion:

  1. The OAS is the same for straight bonds and for bonds with embedded options.

  2. The OAS is affected by assumptions about interest rate volatility, as the embedded options are positively correlated with volatility (both calls and puts increase in value as volatility increaes)

a) OAS=Z-Spread - Call Option

b) OAS=Z-Spread + Put Option

c) OAS=Z-Spread --> for the option free bond

a) = b) = c)

all three are the same according to statement 1) and BenjaminGraham’s original post, and the Z-Spread changes each time.

Now if we make changes to the interest rate volatility as in the question Kotausi posted, the options increase in value and we have:

a) not equal to b) not equal to c)

Now if Z-Spread ignores volatility completely, I guess it does not change with adjustments to volatility and therefore leading to those differences.

So how can we reconcile these seemingly different notions??

#25

I’m not sure I understand the distinction you’re trying to make here.

One calculates a Z spread, just as one calculates an OAS.

#26

When we change our assumed interest rate volatility, we’re still trying to get to the same market price, which is why the OAS changes.

If the interest rate volatility in the market changes, then the price of the bond with the embedded option will change; the OAS can stay the same.

#27

Thanks S2000, I think I get it now but I might need to let this sink in a bit more…

#28

You’re welcome.

There are lots of movable parts. You need to make sure that you’re moving the ones that should move, and leaving the others alone.

#29

Agreed!!

#30

Just a quick question regarding this topic. If it is given a binomial tree for a straight bond, and then it’s given an OAS for a callable bond.

To calculate the callable bond, I just add the spread to each interest on the tree and I recalculate it (taking into account if it’s called or not).

If then I have to calculate a identical putable bond, do I do the same (adding the same OAS at each interest) but just taking into account if the bond it’s put?

#31

That’s it in a nutshell.

#32

perfect, thank you magician.

#33

Thanks for the read guys, this is a great thread.

#34

You’re quite welcome.