# Effect of volatility on OAS (LOS 44 h)

Hi guys,

CFAI Curriculum explains that increasing volatility decreases the OAS for a callable bond. I cannot grasp this explanation. My reasoning is that the OAS is by definition the spread added to the one-period forward rates on the interest rate tree. In other words, OAS is added to the discount factors. If the discount factors is equal to 1/(1+r), then adding OAS would result in 1/(1+r+OAS). OAS increases the discount rate, thus making the future cash flows lower. Lower cash flows translate to a lower bond price.

On the other hand, volatility increases the option values, thus decreasing the value of the callable bond. If the value of a callable bond is lower, then the sum of the cash flows should be lower, hence higher discount rate. This seems in line with increasing OAS, rather than decreasing.

What’s wrong with my logic?

What’s wrong with your logic is that you say that OAS increases the discount rate, thus making the future cash flows lower. Changing the discount rate doesn’t change the cash flows. It does, however, change the present value of the (unchanged) cash flows.

Try thinking about it this way:

• When a bond is called, the cash flow at that node is decreased.
• The greater the volatility of interest rates, the more likely it is that the bond will be called, so the greater the number of nodes at which the bond is called, and the greater the average decrease at each node where it is called.
• Therefore, the greater the volatility of interest rates, the lower the average cash flow.
• The lower the cash flows, the lower the discount rate needed to get the same present value. (This is key: the market price of the callable bond doesn’t change merely because we change the volatility in our model.)
• The lower the discount rate, the lower the spread.

In short: higher volatility, lower cash flows, lower discount rate, lower OAS.

For a putable bond, putting the bond increases the cash flow at that node, so: higher volatility, higher cash flows, higher discount rate, higher OAS.

Thanks for the explanation. I think I get the point now. The PV of the future expected CFs decreases due to the higher probability the bond to be called resulting from the higer volatility assumed_._ What about the market price of the callable bond? Does it remain unchanged? If so, then it makes sense the discount factor to decrease and the only source of the reduction would be the shrinking OAS.

My logical flaw was that I was always thinking that the market price of the callable bond isn’t fix but changes with the PV of future expected CFs.

The market price is the market price; the market doesn’t know about our binomial tree (and wouldn’t care about it if it did). We’re guessing at the volatility of future interest rates, and computing an OAS based on our guess. The only things that change are our guess about the volatility of interest rates, and the resultant OAS we calculate.

s2000magician - i can argue that if interest rates increase noting happens to the OAS, as the OAS is not affected by interest rates because we are removing the optionality. so nothing happends could also be the right answer, right?

Yes. In fact, that’s just what we do when computing the effective duration of a bond with embedded options.

Of course, if interest rates increase and the OAS doesn’t change, the price of the bond will decrease.

S2000magician -

Having problems with this still after reviewing it: S2000, where is my logic wrong?

Callable bond:

As volatility increases in our model, the likelihood of being called and giving the investor its money back increases, therefore yields decrease (your overall return decreases). Since the discount rate is smaller so is the OAS spread.

As volatility decreases in our model, the likelihood of the bond being called decreases, you get more cash flows and therefore your yield increases as well as the OAS spread

Putable bond:

As volatility increases in our model, the likelihood of being put and giving the investor its money back increases, therefore; the investor, although receiving its money back will not receive the remaining cash flows, which to mean means, lower yields and lower

As volatility decreases in our model, the likelihood of being put and giving the investor its money back decreases, therefore; the investor will receive all of its promised cash flows and have a higher yield and higher OAS.

The flaw is in thinking that when you put a bond your yield is lower.

Why would I exercise an option that makes me worse off?

but wouldnt your yield be greater if you held the putable bond till maturity as supposed to getting your money back sooner and forgoing all the remaing cash flows?

Not necessarily.