Question

. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option?

Answer 1

The value of each call option is $1.6.

Step-by-step explanation:

The formula for the risk-neutral probability of an up movement is

p =
`(e^(rT) -d )/(u - d)`

u = 36 / 30 = 1.2

d = 26 / 30 = 0.8667

r = 0

T = 0.5

The formula gives :

p= (1-0.8667) / (1.2-0.8667) =0.4.

The payoff from the call option is $4 for an upward movement and $0 for a downward movement.

The value of the option

=0.4×4 +0.6×0 = $1.6