Pg 28 #12.17 (b) - Answer to Hull Chapter 13: Binomial Trees (Hull Text)

[Dr. Jayanthi Sankaran]

Hi David,

I have posted my question as a new thread because there is no associated Student Forum:

The Binomial Tree in the third middle node has $39.6 as the stock price. I have redone the tree using $40 as the value in the third middle node. Isn't it conceptually wrong to have $39.6 instead of $40?

Thanks!
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran

That's John Hull's question. Note the assumption given is Over each of the next two three-month periods it is expected to go up by 10% or down by 10%; i.e., it's the simpler arithmetic +/- 10% rather than the (effectively) lognormal implied by exp(10%*t). In this case, while the arithmetic average of (+0.10, -0.10) equals zero, the geometric average is less than one. That said, yours would not be conceptually wrong as your tree would also recombine, but it implies that d = 1/u such that ud = u*(1/u) = 1 whereas (1+x)*(1-x) = 1 only works if x = 0. I hope that helps,

 

[Dr. Jayanthi Sankaran]

Thanks David - appreciate it!

Jayanthi