A stock is currently selling for $26.50. A 2-month put option with a strike price of $30 has an option premium of $4.15. The risk-free rate is 2.5 percent and the market rate is 9.75 percent. What is the option premium on a 2-month call with a $30 strike price? Assume the options are European style.
A) $0.00
B) $0.33
C) $0.41
D) $0.67
E) $0.77

Question

Quizplus · Accepted Answer

The correct answer is E.The call option premium can be calculated using the Black-Scholes formula:C = S * N(d1) - K * e^(-r * t) * N(d2)where:S = stock price = $26.50K = strike price = $30r = risk-free rate = 2.5%t = time to expiration = 2 months = 1/6 yearsigma = volatility = 9.75%d1 = (ln(S/K) + (r + sigma^2/2) * t) / (sigma * sqrt(t))d2 = d1 - sigma * sqrt(t)N(d1) = 0.6700N(d2) = 0.5000C = $26.50 * 0.6700 - $30 * e^(-0.025 * 1/6) * 0.5000C = $17.75 - $17.34C = $0.41Therefore, the option premium on a 2-month call with a $30 strike price is $0.41.

A Stock Is Currently Selling for $26