Question

Andover's stock is currently selling for $40.00 a share but is expected to either decrease to $36 or increase to $44 a share over the next year. The risk-free rate is 4 percent. What is the current value of a 1-year call option with an exercise price of $42? $1.18 $1.27 $1.35 $1.46 $1.59

Answer 1

Hi,

Here S0=$40

X=$42

Possible upside of share= $44

Possible downside of share= $36

risk free rate = 4%

Let us assume that it is possible to equate the value in both the up and the down situation. So, long delta shares and short 1 call option. In the situation of the price being 44 on maturity, the option gives a value of $2, and the long position gives the value of the stock. Hence, the total value of the portfolio is (44delta − 2).. Ιn case the price is 90, the option has zero value, and the long position has value equal to 36delta. As we assumed both these values are the same, therefore:

44*delta-2=36*delta

8*delta=2

delta= 2/8= 0.25

Hence full portfolio after one year = 25*36= $900

Value of portfoliio today = 900/e^0.04

=900/1.04= $864.7

hence

25*40-c*100=864.7

c*100=1000-864.7= 135.3

c=135.3/100= $1.35

Hence $1.35 is the right answer

Thanks