Suppose if anlayst assumes the lower than actual level of volatility, the callable bond will appear to have higher than actual level of OAS - can anyone explain this ?
Also, can you please explain what this formula says : OAS = Z-spread - option cost
Think of a binomial tree. The greater the assumed volatility, the wider the future price swings, so the more likely that the bond will be called; the smaller the assumed volatility, the narrower the future price swings, so the less likely that the bond will be called.
When the bond is called, the bondholder receives a lower cash flow than he would if the bond weren’t called. Therefore, the greater the assumed volatility, the lower the future cash flows; the smaller the assumed volatility, the higher the future cash flows (though never greater than for a noncallable bond).
The lower the cash flows, the lower the discount rate required to get a specified PV: today’s market price; the higher the cash flows, the higher the discount rate. The lower the discount rate, the lower the spread (OAS) added to the treasury rates; the higher the discount rate, the higher the spread (OAS) added to the treasury rates.
So:
(I encourage you to go through the same sequence for putable bonds.)
Switching gears . . .
Z-spread is the spread – additional yield above that of a risk-free bond – paid to cover all risks, including option risk. OAS is the spread – additional yield above that of a risk-free bond – paid to cover all risks _ except _ option risk. The difference, therefore, is the spread to cover exactly the option risk: it’s the price of the option, measured in basis points of yield.
S2000magician - Thanks for all your great help!!!
You’re quite welcome.
that was great. Thanks a ton!
one small doubt - when you say higher/lower CF’s, you mean re-investment component -right ?
No. I mean that when the market value (of the option-free bond) is $1,160.36 and they call it at $1,100, you get less cash than you would if you could sell the option-free bond in the market.
You’re quite welcome.
Comment here:
Higher Vol–> higher probability of being called–> lower cash flows–> **Higher Discount**
Lets assumed you have a 3 year bond called in year 2 at par. Now lets assume the its market price is $110. If it gets called in year two its market price will be $105. So wouldn’t you use a higher discount to get it down to its market price?
We’re talking about the market price today; we have no idea what the market price will be in the future.
If it’s called in year 2 then you have a lower cash flow in year 2. You’re discounting that year 2 cash flow back to today to get today’s price. If the cash flow is lower, you need a lower discount rate to get to today’s price.
Could you give an example with numbers please?
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Hi, i am clear till lower discount rate, lower OAS. part, so if the discount rate is lower, why is the discount rate OAS not Z, and if your put option is included in the Z, how do you make decision on OAS???
If you’re discounting a cash flow of $100 to get a present value of $50 you need a higher discount rate than you need if you’re discounting a cash flow of $90 to get a present value of $50.
With the same underlying forward rates, a higher discount rate requires a higher spread.
The Z-spread doesn’t remove the value of the option; the OAS does. If you’re trying to compare the value of an option-free bond to that of a bond with options, you need either to add option value to the option-free bond or remove the option value from the bond with options; OAS does the latter.
the higher the rate the more likely you will mistaken current call option bond is over priced?
and also how this work for puttable bond