how do volatility assumptions affect OAS?

In the Z-spread, volatility is assumed to be zero because the change in volatilities affect the embedded option.

OAS removes this embedded option, so what is the connection between volatility and OAS?

OAS = z-spread - option cost

Increased volatility will increase the cost of the option, leading to a lower OAS.

You have to assume z-spread is constant/fixed, then the increased volatility will increase costs of options and reduce OAS for a call option and the oppositve is true for a put option:

OAS = z-spread - option cost (call) OAS = z-spread + option cost (put)

Also consider prepayment options (owned by the issuer) and conversion options (owned by the bondholder)

My understanding:

OAS is the value of the security WITHOUT the option, so option volatility should not impact OAS value.

OAS = z-spread - option cost (call)

But of course, if z-spread is constant while volatility increases, it means that its credit or rate component changes by the same amount. So technically the increase in OAS is due to this credit/rate component and not the option cost.

Correct me if i’m wrong.

Correct: OAS should not change with interest rate volatility; Z-spread and option cost should change.

(Note: in the real world, probably both OAS and Z-spread change somewhat.)

From Schweser book 2 exam 2 morning session #46

"The OAS removes the yield difference due to the features of the embedded option, and leaves a spread that reflects the difference in credit risk and liquidity risk. Since in this case the credit risk of the bonds is similar, the OAS could prove helpful in evaluating the relative liquidity risk. OAS will be affected by different assumptions regarding the volatility of interest rates."

magician?

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Can you please explain the post above that says: OAS = z-spread + option cost (put) I thought it was always OAS = z-spread - option cost.

All else equal, you will, in fact, get a different value for OAS under different assumptions about interest rate volatility.

However, that’s a somewhat unfair conclusion, because if the volatility of interest rates changes, all else will not be equal: the market price of the bond will change. And, in theory, it should change by an amount that exactly offsets the change in the value of the option, leaving the OAS the same.

Can someone please explain OAS = z-spread + option cost (put) i remember it always as z-spread - option cost.

You are long the put option, so it adds value to your position. This has the effect of reducing the required spread. So you are subtracting a negative (adding a positive).

So from the perspective of the bondholder, since the put adds value, its option cost is <0, as a result, OAS = z-spread - (-option cost) which is OAS = z-spread + option cost Is that right?

OAS = Z-spread – option cost, always.

Options that favor the issuer (call options, prepay options) have positive option cost; options that favor the bondholder (put options, conversion options) have negative option cost.

So if volatility increases option cost rises for the issuer and leads to lower OAS. On the other hand from the perspective of the bond holder if volatility increases the option is in his favour and increases value of option and so higher OAS?

Can an up please confirm . Thanks

OAS is not affected by volatility of interest rates, since the option is the part that is affected by interest rate volatility and OAS is the part of Z spread that has the option effect removed.

an increase in interest rate volatility increases the VALUE of both the call option and put option. HOWEVER,

an increase in the value of a call option would make the bond less valuable and hence would lead to a lower price in a callable bond.

an increase in the value of a put option would make the bond more valuable and hence would lead to a HIGHER price in a putable bond.

to summarize, increase in interest rate volatility:

does not affect and option-free bond.

decreases the price of a callable bond.

increases the price of a putable bond.

hope i’ve answered your question right.

It’s option and the option cost that change with volatiity but if we look at the formula these two effect oas that is my understanding are we saying the same thing?

Just to clear everything up for people still wondering about the relationship between interest rate volatility and OAS:

There is an inverse relationship.

Higher Interest Rate Volatility decreases OAS

Lower Interest Rate Volatility increases OAS

From Volume 5, Reading 47:

As with the value of a bond with an embedded option, the OAS will depend on the volatility assumption. For a given bond price, the higher the interest rate volatility assumed, the lower the OAS for a callable bond. For example, if volatility is 20% rather than 10%, the OAS would be –6 basis points. This illustration clearly demonstrates the importance of the volatility assumption. Assuming volatility of 10%, the OAS is 35 basis points. At 20% volatility, the OAS declines and, in this case is negative and therefore the bond is overvalued relative to the model.

That’s the wrong way to look at it.

If volatility increases the option cost rises, but the value of the bond with the embedded option should change; the OAS should remain the same: the value of the bond _ without the option _ shouldn’t be affected.

hey s2000, could you please clarify if what i said earlier is right?

ie:

OAS is not affected by volatility of interest rates, since the option is the part that is affected by interest rate volatility and OAS is the part of Z spread that has the option effect removed.

an increase in interest rate volatility increases the VALUE of both the call option and put option. HOWEVER,

an increase in the value of a call option would make the bond less valuable and hence would lead to a lower price in a callable bond.

an increase in the value of a put option would make the bond more valuable and hence would lead to a HIGHER price in a putable bond.

to summarize, increase in interest rate volatility:

does not affect and option-free bond.

decreases the price of a callable bond.

increases the price of a putable bond.

there’s just so much conflicting info going on, i just want to know if my way of thinking is right.thanks a ton.

To be clear, they’re talking about the _ calculated _ OAS, not the actual OAS.

Clearly, if you change your assumption about the volatility of interest rates and leave the price of the bond (with the embedded option) _ unchanged _, the OAS you calculate will change. That’s not a property of OAS; that’s a property of your assumption. If the volatility of interest rates _ really _ changes, then the market price (reflecting the true volatility) will also change, and the (true) OAS will stay the same.