Value of Bond/Options

When the question say value of a bond, does it mean price of bond or YTM of the bond? I faced questions from Schweser, some when they say value they talk about value of embedded options and in some they mean price of bond. I am confused now.


Can you offer an example?

I couldn’t find the question that made me write this. However, I’ve faced another question with the same problem, here it is.

Sharon Rogner, CFA is evaluating three bonds for inclusion in fixed income portfolio for one of her pension fund clients. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable in two years and bond C is putable in two years. Rogner computes the OAS of bond A to be 50bps using a binomial tree with an assumed interest rate volatility of 15%.

If Rogner revises her estimate of interest rate volatility to 20%, the computed OAS of Bond B would most likely be:

A) higher than 50bps.
B) lower than 50bps.
C) equal to 50bps

Answer is B. The explanation is "The OAS of the three bonds should be same as they are given to be identical bonds except for the embedded options (OAS is after removing the option feature and hence would not be affected by embedded options). Hence the OAS of bond B would be 50 bps absent any changes in assumed level of volatility.

When the assumed level of volatility in the tree is increased, the value of the embedded call option would increase and the computed value of the callable bond would decrease. The constant spread now needed to force the computed value to be equal to the market price is therefore lower than before. Hence an increase in volatility estimate reduces the computed OAS for a callable bond."

In the second paragraph, when they say the “value of the embedded call option” it must be in % terms to make sense for the following line which is “value of the callable bond would decrease”. Here the term value means absolute dollar value. Please correct me if I am not getting these things correct. I am attending my exam on 26th May. I don’t feel so confident. By the way, I didn’t understand the concept of this question either. I know callable bonds are the costliest and putable are cheapest. The OAS works exactly opposite for the both the type of bonds. But don’t know why, this question is not going to my head. If volatility increase, the cost (%) should increase and it should be higher than 50 bps. Why lower? Thanks in advance.