#### BharatSHarma

##### New Member
Hi David,

Got couple of questions on OAS:

1) Can you please explain the difference between Z spread & OAS?
2) Can you help me understand the inverse relationship between OAS & prepayment for Premium tranches and how it is helpful for investor holding them?

Thanks
Bharat

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Bharat,

Both the Z and the OAS are spreads that equate the model-based PV to the observed market price. But the key problem with the "static" Z-spread is that it assumes the bond's cash flows are given; therefore, it cannot handle an embedded option (or, in the case of MBS, a path-dependent embedded call option = prepayment option).

So, the key relationship is option cost = Z spread - OAS; aside from methodological difference (the OAS needs a Monte Carlo), you can see that the value of prepayment option is their only difference (if option = 0, they should equal each other. In technical terms, if no embedded option, the MCS OAS should be an unbiased estimate of Z spread). I think the easiest way to view this is, imagine you could buy a bond with or without a prepayment option. If you'd pay a Z-spread of 80 bps (eg), you'd pay a lower OAS spread (<< 80) if the issuer has a call option. (classically testable FRM concept: mortgagors are like issuers of callable bonds).

2. The inverse relationship is illustrated by above: imagine the prepayment tending toward zero, then the option cost drops as the OAS increases toward the z-spread. I don't want to comment beyond that b/c it gets complicated and premium could refer to CMO senior tranche or price > par.

Thanks, David

#### srinu2singaraju

##### Member
Great explanation David.
Good clarity on fundamental.

#### danghara

##### Member
Hi David, I got confused by the concept Z-spread and OAS.

When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more spread (which is the OAS) for this instrument in order to get more discount on the bond price.

So to me, Z spread should be less than the OAS.

But this is not what has been discussed in the book. Could you please help me to understand this concept?

#### VanBuren77

##### New Member
Hi David, I got confused by the concept Z-spread and OAS.

When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more spread (which is the OAS) for this instrument in order to get more discount on the bond price.

So to me, Z spread should be less than the OAS.

But this is not what has been discussed in the book. Could you please help me to understand this concept?

In this scenario, both the Z-Spread and the OAS should increase. They'll only differ once the interest rate volatility changes.

Think of it this way:

1. The Z-Spread is a single forward interest rate path in which cashflows are projected
2. The OAS is an average of 250+ forward interest rate paths in which cashflows are projected

If we add an option to a bond, the Z-Vol will increase because we need to be compensated for the additional risk of the bond being called.

The OAS will also increase, but not as much. Because there are more interest rate scenarios in which the bond is called. The greater the interest rate volatility, the lower the OAS will be. Yet, Z-Vol will remain unchanged.

Here is a graph explaining the differences in spread. The greater the market volatility, the more valuable that call option becomes.