OAS spread & model pricing question:

[no_ming]

Hi, Mr. Harper, the following question is about OAS and I am confused with the OAS from the question provided.
I know the company spot rate = Treasury spot rate + OAS, however, the question provides that the OAS is -30 below company spot rate and +50 above the Treasury spot rate, is there any contradiction?

 

[Nicole Seaman]

Hi, Mr. Harper, the following question is about OAS and I am confused with the OAS from the question provided.
I know the company spot rate = Treasury spot rate + OAS, however, the question provides that the OAS is -30 below company spot rate and +50 above the Treasury spot rate, is there any contradiction?

View attachment 739

Hello @no_ming

Could you please provide us with the source of this question so David and other members can help you?

Thank you,

Nicole

 

[David Harper CFA FRM]

Hi @no_ming I agree with @Nicole Manley , what is the source?

To me, the question does not contradict: the company's spot rate curve is (on average) about 80 basis points above the Treasury spot rate curve; put another way, the static Z-spread is probably approximately 80 bps. The Treasury spot rate curve represents the risk-free rate and the company's spot rate curve includes the credit spread (compensation for credit risk), among other factors. In this way, we would expect the OAS over the company spot rate (which is higher than risk-free curve) curve to be less than the OAS over the Treasury curve, simply because the company spot rate curve includes credit risk spread that the Treasury spot rate curve.

What I don't like about the answer is that both (A) and (C), at first glance, seem plausible: the OAS can use either risk-free benchmark or issuer's own benchmark. However, I imagine the question is looking for (A) as the correct answer because I suppose it's more natural to assume the "model price" is an attempt at fair value; butI am not actually sure because you can argue for (C) based on an understanding of the relationship between the Z-spread and the OAS. I don't think the question can make an assumption here, but instead should offer at least some hint in the question as to its definition of "model price." (at the risk of a being a Q&A technician, that's the problem: "model price" is introduced only in the answers). Thanks!

 

[no_ming]

Hi @no_ming I agree with @Nicole Manley , what is the source?

To me, the question does not contradict: the company's spot rate curve is (on average) about 80 basis points above the Treasury spot rate curve; put another way, the static Z-spread is probably approximately 80 bps. The Treasury spot rate curve represents the risk-free rate and the company's spot rate curve includes the credit spread (compensation for credit risk), among other factors. In this way, we would expect the OAS over the company spot rate (which is higher than risk-free curve) curve to be less than the OAS over the Treasury curve, simply because the company spot rate curve includes credit risk spread that the Treasury spot rate curve.

What I don't like about the answer is that both (A) and (C), at first glance, seem plausible: the OAS can use either risk-free benchmark or issuer's own benchmark. However, I imagine the question is looking for (A) as the correct answer because I suppose it's more natural to assume the "model price" is an attempt at fair value; butI am not actually sure because you can argue for (C) based on an understanding of the relationship between the Z-spread and the OAS. I don't think the question can make an assumption here, but instead should offer at least some hint in the question as to its definition of "model price." (at the risk of a being a Q&A technician, that's the problem: "model price" is introduced only in the answers). Thanks!

Hi, David, I get it with Z spread = 80 bps, does it mean the option cost is equal to 30? That is :

Company spot rate = Treasury spot rate + Z spread or
Company spot rate = Treasury spot rate + (credit spread + liquidity spread + option cost)
Company spot rate = Treasury spot rate + (OAS spread + option cost)
Company spot rate = Treasury spot rate + (50 bps +30 bps)

By the way, the question is given from my friend and he say that he buy it from internet and share to me~Honestly, do you mind I post this type of questions and discuss in the forum and share with other members?

 

[David Harper CFA FRM]

Hi @no_ming Yes, that is exactly correct, at least in terms of my interpretation. Well done I do think there are some potential nuances here, but let's just imagine this question's scenarios with flat spot rate curves. Let's start by assuming a flat Treasury spot rate curve at 1.0% for all maturities. The Z-spread (aka, zero-volatility OAS) looks to be about 30 + 50 bps = 80 bps, such that, the model price of the non-callable corporate bond is given by a risky spot rate curve at 1.80% (with flat curves, nominal spread equals the Z-spread). Just as you write, the difference is mostly credit spread (compensation for credit risk) but includes liquidity (if not currency) and option cost.

In this example, the market price (versus the model price) appears to be produced by the binomial when the rate curve is 1.50%; i.e. + 50 above 1.0% and -30 below 1.80%. In flat curve terms:

• As Z-spread = OAS + option cost, 1.80% = 1.50% OAS + 30 bps option cost, put another way:
• 1.8% would be earned in the static rate environment, but only 1.5% would earned in the volatile rate environment (i.e., the binomial tree is required to capture the effect of volatility on the call option) such that the cost of the option is 30 bps.

This interpretation, alas, introduces further nuances (questions). For example, is the OAS really 1.5% or -30 bps or +50 bps? (isn't a -30 OAS problematic because it appears to suggest that the introduction of optionality actually increases the bond price by lowering all discount rates). Why is the assumption of upward-sloping relevant? (I do not see how it is). But, IMHO, these are nuances not anticipated by the question.

I really don't mind this type of question merely because it adds to the forum's learnings, thanks!