How to price option with limited information?

Question

You have a call option on a security worth 100 now that will either be worth 110 or 95 dollars at a future date. The strike of this option is 105. What is an estimated value of this call option?

Answer 1

$d=0.95$ and $u = 1.1$

Risk Neutral probability is $\pi_u = \frac{1+r-d}{u-d} = \frac{1}{3}$ assuming risk free rate is 0.0

Then $\pi_d = \frac{2}{3}$

$c_u = 110-105 = 5$ and $c_d = max(95-105,0) = 0$

Thus the value of the call option is $ = \dfrac{\pi_u\times c_u + \pi_d\times c_d}{(1+r)} = \frac{1}{3}.5 + \frac{2}{3}.0 = \frac{5}{3}$