# OAS on callable bond

Wouldn’t the OAS on a callable bond price decrease when the interest rate volatility increases on the bond, which would thus increase the OAS on a bond? Since call option value increase with volatility which would thus decrease the price on the bond.

So with higher volatility leading to a higher option cost, will “reduce” the OAS on a callable bond. The formula for OAS = z-spread - option cost. So a higher option cost will lead to a lower OAS.

Also, the value of a callable bond would go down due to higher volatility and putable bond will go up, which is indirectly suggesting that higher volatility increases uncertainty of cash flows towards investors and issuers.

Hope this helps.

I believe that you’re misunderstanding the situation.

The price of the bond doesn’t change; it’s the market price of the bond. What changes is your assumption about interest rate volatility in your binomial tree. The market doesn’t know about your binomial tree, and if it did know about it, it wouldn’t care.

You need to understand the reasoning behind the OAS as a function of (assumed) interest rate volatility:

• As volatility increases, the high rates in the tree increase and the low rates decrease
• With lower low rates, it’s more likely that the call option will be in the money, so it’s more likely that the call option will be exercised
• When the call option is exercised, the cash flow is lower than when it isn’t exercised
• The more likely the option is to be exercised, the lower the average cash flow from the bond
• If you discount lower cash flows to reach the same price, you need lower discount rates
• Lower discount rates mean that the OAS is lower
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so is the z spread used to compute the market value for the bond, while the OAS is used to compute the appropriate spread on the bond , given the current market price?

They’re each used to compute a spread on a bond given its market price.

The z-spread is appropriate for bonds without embedded options, but not for bonds with embedded options.

The OAS is appropriate for all bonds.

What is the reason for that? It seems the philosophy behind the z spread and the OAS is similar to each other so you would expect them to be the same thing.

What is the reason for what? I don’t understand the question.

I’m not sure what you mean by the philosophy behind them, but if they were the same thing then they wouldn’t need different names.

You do need to understand the differences between them, which I tried to outline above.

I’ve written a number of articles on various spreads, including the z-spread and OAS. It sounds as though you’d benefit from reading them.