Question

Suppose a share of stock sells for $63. the risk-free rate is 5 percent, and the stock price in one year will be either $70 or $80. a. what is the value of a call option with an exercise price of $70? b. Calculate the minimum return on the stock required to get the option in the money?

Answer 1

Current Stock Price = $ 63, Exercise Price = $ 70, Risk-Free Rate = Rf = 5 % and Option Tenure = 1 year, Probable Stock Prices: $ 70 or $ 80

As the probability of the stock's price being $70 or $ 80 is not provided, the same is assumed to be 50% for each outcome (both prices are equally likely).

In case stock price is $ 70, option payoff = $ 0 and in case stock price is $ 80, option payoff = (80 - 70) = $ 10

Expected Value of Payoff = 0.5 x 10 + 0.5 x 0 = $ 5

Call Price = PV of Expected Payoff = 5 / 1.05 = $ 4.7619 ~ $ 4.76

The option will be in the money, if and when the stock's price goes beyond the option exercise price of $ 70. Therefore, for the option to be in the money, the stock price should move from $ 63 to atleast $ 70.

Hence, Minimum Return Required = (70 - 63) / 63 = 0.1111 or 11.11 %