A stock is priced at 38 and the periodic risk-free rate of interest is 6%. What is the value of a two-period European put option with a strike price of 35 on a share of stock using a binomial model with an up factor of 1.15 and a risk-neutral probability of 68%? A) $0.64. B) $2.58. C) $0.57. Show your calculation
Looks like C: [(35-38*.87*.87)*(.32*.32)]/(1.06)^2=.57
cfaboston28 Wrote: ------------------------------------------------------- > A stock is priced at 38 and the periodic risk-free > rate of interest is 6%. What is the value of a > two-period European put option with a strike price > of 35 on a share of stock using a binomial model > with an up factor of 1.15 and a risk-neutral > probability of 68%? > > A) $0.64. > > B) $2.58. > > C) $0.57. > > Show your calculation Just to do all the calculations (even though some are given). Up= 1.15 Down = 1/1.15 -> .8696 (rounded) Up factor -> 1.15*38 = 43.7 Down factor -> .8696*38 = 33.04 B/c its a put we are only interested in the down factor. Prob. of up factor: (1 +.06 - .8696)/(1.15-.87) = .68 (Given) Down factor prob: 1-.68 So now its just X-33.04 = 1.96*(1-.68) =.62.72 Now just discount by Rf rate. B/c its a two tiered we ^2 it. .6272/(1.06^2) ~ .59
C: [(35-38*.87*.87)*(.32*.32)]/(1.06)^2=.56849
Interesting way of doing it, since you know any of the higher results of the tree have a put value of 0. I found 28.73 in the bottom part of the tree for the second period which equates to 6.27 put value (p–) P± has to be zero since we’ll be back at 38 for stock price. So the equation is just, 0.32*6.27/1.06 = 1.89 Now compare P- to P+ P+ is zero again so 0.32*1.89/1.06 = 0.57
If the strick price was a little different, I would assume it wouldn’t be quite that quick
Its simplified by the fact that there’s only 1 scenario in which the put has any value (Down, Down). If it was an in the money put option the calculation would be longer.
still a little confused, if this is a two period option why do we discount the moneyness only after the first period. what if the move is down, down. first move down X-33.04=1.96 second move down X-(33.04*.8696)=6.27. 1.96*(1-.68) =.62.72 6.27*(1-.68)=2.01 Discount both =2.52 Can someone please explain why 6.27 is not used here.