Question

Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $115 or down to $85 in 1 year. The stock does not pay dividend and interest rates are zero. Use the tree to compute the value of a 1-year $100-strike European put option on the stock.

Answer 1

Year 0		Year 1
		115
100
		85
U=115/100	1.15
D=85/100		0.85
P(U) = (1.15-1)/(1-0.85)	50%
P(D) = 1-0.5	50%
Here both upward & downeard have the same probability
Now if value after one year reaches 100 then
Probaility downward with 85 strike price will be used
So here gain will be 100-85 =15
But the probability is 50%
So the value of PUT Option at strike price is 15*50% = 7.5$