A stock is currently priced at $54. The stock will either increase or decrease by 10 percent over the next year. There is a call option on the stock with a strike price of $50 and one year until expiration. If the risk-free rate is 4 percent, what is the risk-neutral value of the call option?

Answer: Value = $6.33

Explanation:

First of all we have to find the risk neutral probability. For that we have to find the up-move and down-move factor. As it is given that the stock will go up or down by 10%, so the up-move factor is 1.1 and down-move factor is. 9. To find the risk-neutral probability the formula is:

π = (1+r-d) / (u-d)

where;

d = down-move factor

u = up-move factor

r = risk free rate

Using this formula you will get the risk-neutral probability 0.7.

To calculate the value of the call option the formula is:

((π*C+) + ((1-π) * C-)) / (1+r)

where;

C + = stock price if it goes up - strike price ((54*1.1) - 50) = 9.4

C - = Stock price if it goes down - strick price (as it goes negative so C - = 0, because the option holder won't exercise the otpion)

And (1+r) is to get the present value.