To calculate the price of the call option, we can use the Black-Scholes formula:
C = S*N(d1) - Ke^(-rt)*N(d2)
where:
- C is the price of the call option
- S is the current stock price
- K is the exercise price
- r is the risk-free interest rate
- t is the time to maturity
- N() is the cumulative normal distribution function
- d1 and d2 are calculated as follows:
d1 = [ln(S/K) + (r + σ^2/2)*t] / (σ*sqrt(t))
d2 = d1 - σ*sqrt(t)
In this case, we are given:
- S = $87
- K = $81
- r = 7% per year, compounded continuously
- t = 6 months = 0.5 years
- σ = 0% per year
Using these values, we can calculate:
d1 = [ln(87/81) + (0.07 + 0^2/2)*0.5] / (0*sqrt(0.5)) = infinity
d2 = infinity - 0*sqrt(0.5) = infinity
N(d1) = 1
N(d2) = 1
Therefore, the price of the call option is:
C = 87*1 - 81*e^(-0.07*0.5)*1 = $9.14
So the correct answer is c. $9.14.