OAS spread

[ps_ricky_son]

hi,

on p.28 of the notes P2.T5. (Bruce Tuckman, Fixed income securities), it says if the market price assumes to be $3,613.25, which is $2.8 less than the calculated model price of $3,616, the OAS turns out to be 10 basis points.

May I know how does this "10 basis points" come out? thanks for answering

 

[David Harper CFA FRM]

Hi @ps_ricky_son The 10 basis points does not have an analytical (i.e., convenient formula-based) solution, in a way similar to how internal rate of return (IRR) or implied volatility are found via iteration: we need to iterate an input (aka, trial and error) until the output matches the number we are seeking (beginning with the end in mind). In the case of the option-adjusted spread (OAS), see below please, the notes are exactly following Tuckman's example in Chapter 7. At first (upper panel), the risk-neutral probabilities inform a discounted price of $3,616.05. Then the OAS is introduced and its key assumption is the observation of a market price which could be anything due to technical factors; here it just happens to be $3,613.25. Then it's a matter of "finding" the + 10 bps that, when added to the 5.50% and 4.50%, return a (discounted) model price which matches the observed price of $3,613.25. I am making the following up, but if the observed price were instead $3,602.08, then we'd need to iterate to find that adding + 50 basis points to the discount rates would return such a lower number, and then + 50 bps would be the OAS that is implied by the observed price of $3,602.08. Mathematically, the expected discounted price is the output, however, the OAS is the right "input" that, when added to discount rates, returns a price that matches the observed market price. So the market price is sort of an input in the sense that we are "goal-seeking" to find that answer. I hope that helps!

P.S> xls i just did is right here, a slight mod of the learning XLS:
https://www.dropbox.com/s/dzjign08rzlcqpb/071419-oas-spread.xlsx?dl=0

 

[ps_ricky_son]

Billion thanks David,
I just wonder if I missed some important concepts. Your detailed reply erases my worried

 

[David Harper CFA FRM]

Hi @ps_ricky_son Sure thing. Your question was good so I mentioned in on LinkedIn and I think my second pass might even be sharper with respect to the analogy to implied volatility; in doing so, I realized that both invert to solve for a risk factor (i.e., spread or volatility) as a function of the price. Nothing profound per se, but I always am trying to sharpen the explanation of difficult ideas like this. (In addition to the idea of inverting a function to solve for a key risk factor, I always try to stress also that whenever we invert, we are using a model, so the whole thing is entirely "model dependent."

Here is how I re-wrote at https://www.linkedin.com/feed/update/urn:li:activity:6556285849393258497

"Today in our forum's Q&A, I'm asked how we calculated a bond's option-adjusted spread (OAS). I analogize to option implied volatility. Both OAS and implied vol invert a valuation model to iteratively solve for an input. In practical terms, both infer a key risk factor from a market price. In analytical option pricing, we often solve for an option's value (the output) as a function of volatility and other input variables: c = f(σ, S, K, ...). But implied volatility inverts the model by goal-seeking to find the particular volatility "input" that returns an "output" equal to the option's market price. To invert is to reverse-engineer an input by assuming the output. Similarly, if our binomial interest rate tree solves for a bond's expected discounted value (EDV) of $95.00 but this happens to be $2.00 more than the actual trading price of $93.00, we find the constant spread (the OAS) that needs to add to rates in our tree so that our model's output value is reconciled with the market's price (note I distinguish between "price" and "value"). We assume the bond price so we can reverse-engineer the additional yield that reconciles such price with our model's value. But we still need to assume a model: if we use a different model, we get a different answer."

 

[Michael Yoon]

Hello,

I have a question about the option-adjusted spread on Tuckman's Chapter 7, Term Structure Models.

I have known OAS as the spread that the option cost is eliminated from the Z-spread.

But on the Tuckman's text, OAS is introduced as the spread that makes the model price equal to the market price.

If someone can explain the real definition of OAS, it would be super thankful.

And also, I did not get why Tuckman explains OAS and about its Profit and Loss in the chapter 7. Thats because I have known that to compute the OAS, using the binominal tree is limited and practically Monte Carlo Simulation is used.

Thanks for all who would comment on my question and thanks to DAVID, your video is so helpful for me to study the Tuckman's by myself.

 

[Matthew Graves]

Nothing you have said is incorrect. OAS is usually derived via a Monte Carlo approach as the flat spread which can be added to underlying curve in order to bring the Monte Carlo expected price equal to the observed market price. For bonds with no optionality the OAS will be very close to the Z-Spread.

 

[Michael Yoon]

May I ask you furthermore?

Before I read the Tuckman's Chapter 7, I have known the OAS as the spread that Option cost is eliminated from the Z-spread. So in the case of the callable bond, OAS is a spread of the option-free bond and the US Treasury.

But Tuckman explains the OAS as the added spread that equals the model price and that of the market. I don't get the connection of theses two concepts.

Thanks a lot for answering.

 

[David Harper CFA FRM]

(@Michael Yoon consolidating your different posts on essentially the same topic to one location here. I'll reply when I have time ... Thanks, David)

 

[Matthew Graves]

Ok, so consider an example of a callable bond with market price P. The Z-Spread calculation takes the cashflows for this bond as if it is a non-callable, vanilla bond to arrive at a Z-Spread value which brings the model price equal to P. Obviously, because the bond is callable, there is a non-zero probability that you will not receive some of the cashflows because of the inbuilt optionality. The OAS calculation takes this into account in the Monte Carlo simulation as some simulation paths will result in the bond being called. If P is the same for both calculations you would expect the OAS to be less than the Z-Spread. Intuitively, there is a non-zero probability you will not receive some of the cashflows due to the optionality so the amount of discounting required to arrive at the same market price is less.

 

[Headfield]

@Michael Yoon: Maybe a further way to explain it:

1. The general principle of calculating the z-spread and the OAS are the same.

2. Principle:

a) Assuming, you have a risk-free bond A and assuming, the world is deterministic i.e. we know all future states regarding their risk-free spot-rates and the according probabilities (i.e. the possible paths in the tree model), you would use this model to discount all future cash flows to calculate the present value. Assuming, all assumptions are correct (double here ;-)), your calculation will match the market price of bond A.

b) Assuming, you have a bond B with an IDENTICAL cashflow structure of bond A and we are still in a deterministic world (to simplify the concepts). However, bond B is NOT risk-free and its market price is lower than that of bond A. If you use the same model as for bond A, you will again get the present value of bond A - obviously wrong. To correct this and to include the fact, that bond B is NOT risk-free, you add the z-spread to all of your risk-free spot-rates in your model, until you match the actual market price of bond B. In this way, the z-spread stands for the additional interest rate needed, as this bond is NOT risk-free.

c) Assuming, you have a bond A with an IDENTICAL cashflow structure of bond A and we are still in a deterministic world. However, bond C has an embedded OPTION and its market price is lower or higher (lower, if it is an option for the investor, higher, if it is an option for the issuer) than that of bond A. If you use the same model as for bond A, you will again get the present value of bond A - obviously wrong. To correct this and to include the fact, that bond C has an OPTION, you add/substract the OAS-spread to/from all of your risk-free spot-rates in your model, until you match the actual market price of bond C. In this way, the OAS stands for the additional/less interest rate needed, as this bond has on OPTION.

3. Both approaches work more or less the same way. In fact: Assuming, that you got bond C wrong, i.e. bond C does not have an option but is identical to bond B, than your OAS calculation in c) will be the same als your z-spread calculation in b). Both concepts calculate a spread that is needed in addition/substraction to the risk-free spot-rates to get your calculation of the present value in line with the market price.