# bonds with a binomial interest rate tree

Dear All:

I tried to read the concept of calculating the bond with binomial interet rate tree but I can’t find the rationale behind the rule . I would highly appreciate if you all could give some explanation.

Thank you so much for your time.

Regards

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It’s more for callable bonds, or bonds with some sort of embedded option. You need to see the possibilities in the next period (nodes of the tree) in order to determine the optimal action today. Do you have any specific questions? It’s hard to just give a broad answer that is somehow different from what the book says.

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Dear :

why use the call price if the call price is less than the discount value in the example below.

thank you so much for your time.

A callable bond with an 8.2% annual coupon will mature in two years at par value. The current one-year spot rate is 7.9%. For the second year, the yield-volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The call price is 101. Using a binomial interest rate tree, what is the current price?

A)100.558.

B)101.000.

C)100.279.

Your answer: A was incorrect. The correct answer was B)101.000.The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value for all the nodes in nodal period 2: V

_{2}=100. In nodal period 1, there will be two possible prices:V

_{1,U}=[(100+8.2)/1.076+(100+8.2)/1.076]/2 = 100.558V

_{1,L}=[(100+8.2)/1.068+(100+8.2)/1.068]/2= 101.311Since V

_{1,L}is greater than the call price, the call price is entered into the formula below:V

_{0}=[(100.558+8.2)/1.079)+(101+8.2)/1.079)]/2 = 101.000.You use the call price because the bond will be called – the bond issuer pays less than what the bond is worth to buy it back from you.

Like aaronhotchner said it is most likely that the bond will be called because the option will be in the money for the option holder (the issuer) as he has the right to buy the bond and he’d surely exercise it when he’d be buying the bond at a price less than its worth.

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