You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $116 and a 50% chance of decreasing to $84. The risk-free rate of interest is 8%. Calculate the call option’s value using the two-state stock price model.

The answer is "11.11"

Explanation:

Given values:

The chances of increasing value by 50% is = 116

The chances of decreasing value by 50% is = 84

So, the two possible stock prices are:

S+  = 116 and S- = 84

The exercise price is = 100 so, possible called value are

Chance of increase (Ci) = 116-100 = 16

Chance of decrease (Cd)= 84 -100 = -16   it is - value that's why we avoid this so it equal to 0.

Formula:

edge ratio =      

To develop a risk-free makes the image of one stock share and dual calling in paper. The actual cost of risk-free image is = exercise price- 2C0

= 100 -2C0

= 84 after some years.

The given value is = 84

time = 1 year

interest rate= 8%

interest:

if the edged position is equivalent to the actual payout cost:

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%