Question

Let's say the shares of a stock are currently priced at $61. The future price is estimated at either $52 or $62. The risk-free rate of return is 4%. What is the value of a twelve-month call option with a strike price of $55?

$6.00 $12.00 $6.19 $7.70 $5.48

Answer 1

Ans) 7.70 $

Here So = current stock price = 61$

Sou = possible upside price of stock = 62$

Sod = possible downside price of stock = 52$

r = rate of interest = 4%

u = Sou/So
=62/61
=1.0164

d= Sod/So
=52/61
=0.8525

P = probability = e^rt - d / u - d
= e^4% - 0.8525 / 1.0164-0.8525

= 1.04-0.8525 / 0.1639

= 0.1875 / 0.1639

= 1.144

i.e 114.4 %

Thus value of call option = (Fu x Probabiliy) / (1+r)

= 7 x 114.4% / (1+4%)

= 8.008 / 1.04

=7.70 $