Question

. The price of Dimension, Inc. stock will be either $65 or $87 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent. Suppose the current price of Dimension stock is $70. What is the value of the call option if the exercise price is $70 per share?

A. $6.26

B. $8.48

C. $11.58

D. $15.39

E. $17.62

Answer 1

At the end of 6 months, the value of the call option will be either $17 (if the stock price is $87) or $0 (if the stock price is $65).

Let us consider a portfolio :
+ Δ : shares
-1 : option

The value of the portfolio is either 87Δ - 17 or 65Δ

65Δ = 87Δ - 17

=> Δ = 0.773

The value of the portfolio is certain to be 87*(0.773) - 17 = 50.251. For this value of Δ, the portfolio is hence riskless

The current value of the portfolio is 70Δ - f

where f is the value of the option. Since the portfolio must earn the risk-free rate of interest,

=> (70*0.773 - f)e^0.05*1 = 50.251

=> f = 6.30

Hence, the correct option is (a) $6.26