An analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following data: Given this information, the analyst then calculated the following necessary components of the Black-Scholes model:
N(d₁) and N(d₂) represent areas under a standard normal distribution function. Using the Black-Scholes model, what is the value of the call option?

Question

An analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following data: Given this information, the analyst then calculated the following necessary components of the Black-Scholes model:

N(d₁) and N(d₂) represent areas under a standard normal distribution function. Using the Black-Scholes model, what is the value of the call option?

Quizplus · Accepted Answer

Using the Black-Scholes model, the value of the call option is calculated as:

C = S*N(d1) - X*exp(-r*T)*N(d2)

where:

S = 87.50 (stock price)
X = 90.00 (strike price)
r = 0.02 (risk-free interest rate)
T = 0.25 (time to expiration)
σ = 0.24 (volatility)
d1 = (ln(S/X) + (r + σ^2/2)*T) / (σ*sqrt(T)) = 0.4701
d2 = d1 - σ*sqrt(T) = 0.2822

N(d1) = 0.6804 (from standard normal distribution table)
N(d2) = 0.6119 (from standard normal distribution table)

Therefore:

C = 87.50*0.6804 - 90.00*exp(-0.02*0.25)*0.6119 = $3.47

Thus, the best choice is C.

An Analyst Wants to Use the Black-Scholes Model to Value