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I'm struggling a little with the interpretation of option adjusted spread on mortgage backed securities. I can see how, for a corporate bond without optionality, the z-spread is sort of like a constant hazard rate of default.

  1. Is it right to think of OAS as the constant hazard rate of default on a corporate bond with optionality?
  2. Can I think of the z-spread on a corporate bond with optionality as a constant hazard of non-payment due to either default or option exercise? (I think this isn't quite right because in event of option exercise the principal is paid).
  3. Can I think of (z-spread - OAS) as a constant hazard rate of option exercise?

Underlying these questions is my confusion about what is being accomplished by including OAS in the different interest rate scenarios when modelling the option. In which states of the world is the option expected to be exercised? Is it those states when it is optimal to do so according to the scenario's zero-coupon rate? Or is it those states when it is optimal given zero-coupon rate plus OAS?

My next confusion is how OAS deals with the fact that the option isn't exercised exactly when it is optimal. For corporate bonds there is the issuer's cost of refinancing to consider.

  1. Is this, in fact, exactly why OAS is included in the scenarios for modelling the option -- it is reflecting the refinancing cost that prevents the issuer from refinancing?

On the other hand for RMBS there are numerous causes of prepayment including time-varying macro factors and behavioral factors.

  1. If the answer to #1 above is affirmative, then (a) does that interpretation also hold for agency RMBS which are guaranteed? and (b) if so, why isn't OAS just the same as the spread on an agency bond?

If the answer to #4 is affirmative, then by analogy it would seem for agency RMBS the OAS should capture all deviation of realistic mortgage prepayment (due to all causes) from purely optimal refinancing (ignoring house sales etc.) If that's right then the answer to 5(a) is "no". Maybe for a callable corporate bond the OAS represents the credit spread reflected in the price after adjusting for the value of the call option -- the spread the bond would have with the option stripped out. But for agency RMBS it's clearly not the spread on a hypothetical MBS where prepayment is stripped out because OAS would seem to go up when home owners are for some reason less likely to prepay and go down when for some reason home owners are more likely to prepay.

  1. Is there any intuitive interpretation of OAS on agency RMBS e.g. in terms of hazard rates, or as the spread on some hypothetical instrument?
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  • $\begingroup$ I have to say, I find the interpretation of OAS as a default rate a little strange and hard to comprehend. IIRC I have not seen it before. For one thing the spread can in theory be positive or negative, unlike a default rate. But I am not an expert in these matters. $\endgroup$ – noob2 Jul 7 '17 at 6:49
  • $\begingroup$ Naively, I think of OAS as a measure of market inefficiency: Assuming your model is correct (always a big assumption) the OAS is the rate at which you can earn "free money" by being long this security and short the dynamic model replication of it (optimally executed of course, no mistakes in exercising, no transaction costs). If OAS is negative you would do the opposite, short the security and long the dynamic replication.More realistically, it is not "free money" but compensation for some factors that my model does not take into account. Does this make sense? $\endgroup$ – noob2 Jul 7 '17 at 8:41
  • $\begingroup$ For the case of a callable bond I think that replication is long a bond stripped of the option and short a call option on the stripped bond. As explained in Pedersen "Explaining the Lehman Brothers Option Adjusted Spread of a Corporate Bond" this doesn't fully hedge when you are short the callable and long the replication because your short call option could be exercised and the bond issuer choose not to call the bond. I guess the "factor your model does not take into account" is the issuer's cost of issuing a new bond. Isn't this primarily the issuer's credit spread ~= OAS? $\endgroup$ – David McArthur Jul 7 '17 at 16:08
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In fact, OAS reflects none of the factors mentioned in the question.

To begin with, the technical interpretation of OAS is that is it is the free money you earn for holding an MBS, for the following reasons:

1). OAS has nothing to do with default, as your cash flows are already default-adjusted by your credit model.

2). Similarly, OAS has nothing to do with prepayment, as your cash flows are already prepayment-adjusted by your prepayment model. (That's why OAS is called an option-adjusted-spread, because the spread does't contain any option cost in it.)

As you can see, OAS is adjusted for credit and prepayment. For an (non-agency) MBS, it is subject only to default risk and prepayment risk on top of a treasury, which means, OAS is a measure of the risk-free spread for holding an MBS!

Then, you may ask, if OAS is risk-free spread, how come OAS is not 0 if the market is efficient? There are a few reasons.

1). There is a liquidity consideration for most mortgage bonds. So OAS is above zero to compensate for illiquidity.

2). OAS is very model-dependent. As you can see, the calculation for OAS depends on your credit model, prepayment model, and OAS model (which means interest model as well as home price model). For instance, if your credit model under-predicts losses, then your OAS may be way above 0.

3). There is model risk. An assumption in OAS model is that your cash flow projections are correct. However, as we have discussed, these projections are model dependent and no models are completely correct! Mortgage traders are aware of this risk of the models being wrong, so part of the positive OAS can be attributed to the reward for taking this model risk.

In fact, few practitioners interpret OAS as free money. Rather, they use it as a relative value measure to compare mortgage bonds.

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  • $\begingroup$ think the logic is a little bit inverse regarding liquidity and model risk. yes they are factored in if you take some market data and try to bootstrap an OAS, and imbalanced/one-sided market data may distort your OAS to a positive value (or possibly negative if using the ask price?). However, to me the liquidity and model risk is more reflected in bid/ask spread. Assuming an efficient market and we are confident about the mid, then liquidity and model risk shouldn't be part of OAS bootstrapped from mid. I agree with model dependency and the rest of your answer tho. $\endgroup$ – Will Gu Apr 27 '18 at 5:57
  • $\begingroup$ @WillGu You are right that part of illiquidity is reflected in bid-ask spread. However, when investors buy MBS, they will require a reward for this large spread, and this reward is reflected in OAS even if you use ask (because investors buy MBS at ask). Moreover, if you use ask for MBS, maybe you would want to use ask for Treasury as well. Given exactly the same cash flow, dealer will not ask higher for mortgage than for treasury, if mortgage is less liquid. So even if you use ask, part of OAS is still illiquidity. $\endgroup$ – Harry Lijia Qin Mar 14 at 18:53
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OAS is the fudge compensation factor that falls out in modeling MBS when you don't model expected cash flows (prepayment sensitive) in Risk-Neutral space. Your analogy to corporate default hazard should be interpreted in that light.

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