HFIS - Chapter 34

[toomuchtime]

In Chapter 34 of HFIS, they go through a "binomial interest tree." The tree for bonds without options is very straightforward. However, the tree for bonds with options was a little confusing. I am confused about whether or not the V (Value of the bond) at all nodes except the root changes when a bond is called at a position further to the right. They simply crossed out the value and replaced it with the face amount (call or put price) when the value was greater or less than the call or put price respectively.

I don't have the book in front of me, but I remmeber a tree (Exhibit 34-11??) where the bond would have been called at Node N(sub)LL. They simply replaced the Value at that node with $100. At node N(sub)L, they they replaced the Value with $100 again, without recalculating V(sub)L.

What would have happened had the call at Node N(sub)LL had brought the value at Node N(sub)L below $100?

[Exam Slave]

The bond is called at a node only when it's optimal. That's an assumption. It doesn't have to be the bottom node, though that's a more likely place than the top of the tree.
In Ex 24-11, for example, at N-sub-HL V = 99.732. So the bond is not called, since it would cost 100 to call it. It's not the node; it's the price at the node that determines call or not-call.
As this subject is a real possible question for an exam, you should understand it as well as possible for the exam.

[toomuchtime]

Exam Slave, thanks,

I just looked in the book again, and I think I answered my own question. When I asked, I was thinking about node N(sub)L.

In Exhibit 34-10 (optionless bond), the value at that node is 101.333= (.5*(99.732+100.689+5.25+5.25)/1.04074). I thought that they simply switched 101.333 with 100 in Exhibit 34-11. I didn't realize that they revalued the bond in Exhibit 34-11 (i.e., switching 100 for 100.689 in the formula above) - resulting in a new value 101.002. I thought they just took a tree from an optionless bond and switched anything greater than 100 with 100. This results in a different calculation for node N(sub)L - 101.002

Since this is a callable bond, they replaced the new PV (101.002) with 100, since 100 is cheaper to pay than 101.002.