# Binomial Tree American Put example

#### Eustice_Langham

##### Active Member
Hi David, I have a question concerning the example that appears in the Hull reading on page 287, Figure 13.10. I have attached a screenshot.

I am able to calculate the size of an up move factor, and down move factor as 1.35, .741 respectively, and the risk neutral probabilities of both up and down moves as .490 and .509 respectively.

I calculate the correct forward values:

U = $67.5, D =$37.04
UU = $91.13, UD =$50 and DD = $24.55 and terminal values of$0, $2 and$24.55 respectively

I however get different values for nodes B and C, as:

Node B: exp -.05 * sqrt (1) * (0 * .490) + (2 *.509) = $0.96 Node C: exp -.05 * sqrt (1) * (2 * .490) + (24.55 * .509) =$12.80

then at Node A my values will be different.

I have two questions:
1. are my calculations correct (its not just down to rounding differences) and
2. when considering American options, you need to consider two aspects/calculations..a. how much of the option is worth if exercised at the node AND b. how much is the option worth if not exercised. My question is then how do you make the comparison if the option should be exercised early or not? Thanks

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