Question

Call options with an exercise price of $125 and one year to expiration are available. The market price of the underlying stock is currently $120, but this market price is expected to either decrease to $110 or increase to $130 in a year's time. Assume the risk-free rate is 6%. What is the value of the option?

Answer 1

First of all lets find probability of up move

Probability(P) = ert - d / u - d

u = Su/So

Su = expected increased price = $130

So = stock price = 120$

u = 130/120

=1.08333

u = Sd/So

Sd =Expected decreased price = 110$

u = 110/120

=0.9167

Thus Probability = e6% - 0.9167 / 1.08333 - 0.9167

=1.06-0.9167 / 0.1667

=0.1433/0.1667

=0.8596

ie 85.96%

Thus (1-p) = 1-0.8596

=0.1404

i.e 14.04%

Fu = profit on exercise of option = current market price - strike price

=130-125

=5$

Fd = At price of 110 , option will not be exercised , hence profit from exercise of option = 0

Value of option = [Fu(P) + Fd(1-P)] / (1+r)

=[5(0.8596) + 0(0.1404)] / (1+6%)

=4.2980 / 1.06

=4.05 $