Reading 37 - Embedded Options Bond - LOS H - OAS and assumed volatility

CFA Level II Fixed Income
#1

Hi Guys,

Can someone explain me the intuition behind the following: When an analyst uses a lower-than-actual (higher-than-actual) level of volatility , the computed OAS for a callable bond will be too high (low) and t he bond will be erroneously classified as under-priced (overpriced).

Because I tried to figure out and couldn’t understand. Help would be grateful.

According to me:

In fact, when the volatility is higher-than-actual, the value of the call option will be higher-than-actual => the value of the callable bond should be lower-than-actual. In order to decrease the bond, we need to increase the discount rate and hence the OAS. So for me for higher-than-actual level of volatility, the computed OAS for a callable bond will be too high.

#2

I am still struggling with this myself (so I might be wrong here), but I think both of the statements are incorrect (or should be reversed)

Let’s recall the formula for the OAS first:

OAS=Z-Spread - Option_Value

Now if the volatility used is too low the option value will be lower and we are subtracting less from the Z-Spread giving us a higher OAS.

We use the OAS as a constant added to the forward rates in the tree used for discounting, which means, as the discount rates are higher-> the computed value of the bond at the end will be lower than the actual Value. I would thus conclude that (given that I think that the volatility we used is correct) the bond is overpriced in the market , and my computed value is the correct one (which is lower).

See also the previous discussion:

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91358437

#3

First, remember that OAS is a spread for the bond _ with the value of all embedded options removed _. It’s a spread for a straight bond.

Suppose that the real volatility is 10% and you use 20% in your tree. Then you’re assigning too high a value to the call option. That means that – here’s the key part where you’re stumbling – you’re assigning too _ high _ a value to the straight bond. (Remember that the value of the straight bond is the value of the callable bond plus the value of the call, and you’re using the market price of the callable bond; that doesn’t change. Therefore, if you’ve assigned too high a value to the call option, you’ve assigned a correspondingly too high value to the straight bond.) You need a lower spread to reach a higher value; hence, OAS is too low.

#4

Thanks a lot for both of you for the time taken to answer this.

I appreciate.

#5

My pleasure.