Binomial Question

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I have a question regarding the calculation of binomials:

1. The stock price is currently $80. The stock price annul up-move factor is 1.15. The risk-free is 3.9%. the value of a 2-year European call option with an exercise price of $62 using a two-step binomial model is closest to:

a. $0.00
b. $18.00
c. $23.07 *
d. $24.92 U (up)= 1.15 D (down)= 1__ = 0.8696
1.15

2. A binomial interest-rate tree indicates a 1-year spot rate of 4%, and the price of the bond if rates decline is 95.25 and 93.75 if rates increase. The risk-neutral probability of an interest rate increase is 0.55. you hold a call option on the bond that expires in one year and has an exercise price of 93.00. The option value is closest to:

a. 1.17.
b. 0.97.
c. 1.44.
d. 1.37. *

For question 1) you draw out the 2-step binomial, however, the denominator = e^(0.039*2)

However; for question 2) you do the same, and the denominator = 1+r, where r = .04, the 1-year spot.

Why is this? I've seen this occur several times now in doing practice questions -- both times they are referring to call options, so I'm not sure why the difference. Substituting one for the other (i.e. if i were to use 1+.039 for Question 1), would get me a completely different answer.

Thanks,
Eva

 

[David Harper CFA FRM]

Hi Eva,

So that sounds like the difference between (discrete) annual discounting and continuous discounting (I assume you mean a denominator of EXP(3.9%*1) as you would be discounting from the 1-year nodes, not the two year nodes, in the first question).

If so, it's likely the difference between drawing from Hull (who use continuous throughout) and Tuckman/Jorion (who use, respectively, semi-annual/annual).

As usual in these cases, the question actually should specify; it must specify as neither is right/wrong....

David