Quiz 4-1 in ASM Manual

Hi folks,

I am working on Quiz 4-1 in the ASM Manual (page 87), and had a question.



For an American call option on a stock, you are given:

(i) The stock's price is 52.

(ii) The stock's continuous dividend rate is 10%.

(iii) The option expires in 6 months.

(iv) The strike price is 53.

(v) The continuously compounded risk-free interest rate is .03

The option is modeled with a 2-period binomial tree in which u=1.3, d=.8. Determine the call premium.



So I get the projected end nodes for the stock price are

S_uu = 87.88

S_ud=54.08

S_dd=33.28



I also get the payoffs as

C_uu=34.88

C_ud=1.08

C_dd=0



I also am able to calculate p*, the probability that the stock will go up in price, = .365304.



However when we pull back to nodes u and d,

they use

C_u=[e^(-.25(.03))]* (.365304 * 34.88 + (1-.365304)*1.08) = 13.32696.



Why in this part of the formula:

[e^(-.25(.03))]

Do they not take into account the dividend? When I solved the problem I had used

[e^(-.25(.03-.1))]



Thanks

Quiz 4-1 in ASM Manual