You currently own a one-year call option on RCI stock. The current stock price is $51.20 and the risk-free rate of return is 3.36 percent. Your option has a strike price of $50 and you assume the option will finish in the money. What is the current value of your call option?

Question

Quizplus · Accepted Answer

We can use the Black-Scholes model to calculate the current value of the call option:

d1 = [ln(S/K) + (r + σ²/2)t] / (σ√t)
d2 = d1 - σ√t

Where:
S = current stock price = $51.20
K = strike price = $50
r = risk-free rate = 3.36%
σ = implied volatility (we do not have this information in the question, so we will assume a value of 20%)
t = time to expiration = 1 year

d1 = [ln(51.20/50) + (0.0336 + 0.20²/2)*1] / (0.20√1) = 1.22
d2 = 1.22 - 0.20√1 = 1.02

Using a normal distribution table or a calculator, we find that N(d1) = 0.8907 and N(d2) = 0.8473.

Therefore, the current value of the call option is:
C = S*N(d1) - K*e^(-rt)*N(d2)
C = $51.20*0.8907 - $50*e^(-0.0336*1)*0.8473
C = $2.83

So, the best choice is C, which is the current value of the call option.

You Currently Own a One-Year Call Option on RCI Stock