OAS

CFA Level II
#1

Could someone with a good handle on option adjusted spreads, please help me to understand the following sentence:

“When the assumed volatility in a binomial tree increases, the computed value of OAS will decrease.”

My intuition says the opposite, so I’m clearly missing something?

#2

All else equal (price of option-embedded bond), a higher volatility will make the options more valuable, becuase the cash-flows will fall within the exercise zone more often, and if you increase volatility, but you do not change the price of the bond, then the difference must come from any other spread besides the one with the option. Remember that it’s Z = OAS +/- option spread. Z reflects the final price of the bond, and if the option get’s more expensive (for example, put option on your bond), then the OAS must go up to keep the “spread” the same, since more expensive put options should narrow the Z-spread by increasing in cost, then the OAS must offset it, all else equal. Now that I look at it, OAS can go either way depending on a long put or short call. But since this is probably from an MBS topic, then assume that it’s a callable bond, in which case, OAS goes down.

I did a terrible job of explaining this.

#3

It is true for embedded call

As the volatility increases the value of Call option will increase.

Lets say for an embedded call -> Vcallable = Vstraight - Vcall ,hence Vcallable will go down. So the value the bond is near to the market value hence OAS adjustment will be lower.

#4

I wrote an article on OAS that covers this: http://financialexamhelp123.com/option-adjusted-spread-oas/

The thought process is this: when interest rate volatility increases:

  1. The high interest rates in the tree will be higher, and the low interest rates in the tree will be lower.
  2. The lower the low interest rates, the higher the present value of the remaining cash flows.
  3. The higher the present value of the remaining cash flows, the more likely it is that the bond will be called.
  4. When the bond is called, the lower the cash flow at that node, so the lower the average cash flows for the entire tree.
  5. The lower the average cash flow, the lower the average discount rate needed to get to the same present value.
  6. The lower the average discount rate, the lower the required spread (OAS).
#5

Very helpful - thanks a lot!

#6

You’re quite welcome.