risk neutral probabilities whats the price of a put option

[rbcc]

What is the price of an American-style call option assuming a 2% annual risk free drift, a strike price of 100 with 2 years to maturity. In each year the price can either rise by a foactor of 2 or fall by a foctor of 0.3. The current price an underlying asset that pays no dividends is $100.

what do they mean by "assuming a 2% risk free drift" what's a drift?

 

[rbcc]

is my solution correct?

Using risk neutral probabilities

100(1.02)=p(100*2)+ (1-p)(100*0.70)
102=200p+70-70p
32=130p
p=0.246

p up= 0.246 p down=0.754

so the underlying price is 100 then in time one its either 200 or 70 in time two its either (200*2)=400 or (200*0.7)=140 or (70*0.3)=21

Its a call option so it will be excersied when the price is higher than 100. so the payoffs are (400-100)=300 or (140-100)=40


then the price at time 2 will be (300)(0.246)+(40)(0.754)=103.96 or (140*0.246) +(0)= 34.44

the price at time one is

[(103.96)(0.246)+(34.44)(0.754)]/1.02=50.53

thanks,
rbcc