Dear All:
What is the rationale behind this answer below.
Thank you so much for your time.
Which of the following is the appropriate “nodal decision” within the backward induction methodology of the interest tree framework for a callable bond?
A) Min(call price, discounted value). B) Min(par value, discounted value). C) Max(call price, discounted value).
Your answer: B was incorrect. The correct answer was A) Min(call price, discounted value).
When valuing a callable bond using the backward induction methodology, the relevant cash flow to use at each nodal period is the coupon to be received during that nodal period plus the computed value or the call price, whichever is less.
Par value doesn’t matter if it’s not equal to the call price. The bond will only be called when the call price is less than the discounted value, so obviously C is wrong. B is wrong because you receive the call price when the bond is called. The call price might be set to the par value, but it doesn’t have to be, so B is wrong every time the call price isn’t equal to the par value, and A is always right.
The logic is simple. In the binomial model you assume that the option will be excercised the fist time it makes economic sense. So, once the value of the bond is below the call price the model assumes it will be exercised.
So you always use the calculated value for that node unless the call price is less. In all cases you still assume the coupon is paid so discount the coupon + Min(call, discounted value)