Question

An analAn analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following data: · The price of the stock is $40. · The strike price of the option is $40. · The option matures in 3 months (t = 0.25). · The standard deviation of the stock's returns is 0.40, and the variance is 0.16. · The risk-free rate is 6%. Given this information, the analyst then calculated the following necessary components of the Black-Scholes model: · d1 = 0.175 · d2 = -0.025 · N(d1) = 0.56946 · N(d2) = 0.49003 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?

Answer 1

Value of the call option using Black-Scholes Model is $3.47

Step-by-step explanation:

d1 = 0.175

• d2 = -0.025

• N(d1) = 0.56946

• N(d2) = 0.49003

N(d1) and N(d2) represent areas under a standard normal distribution function.

Stock price: $40.00 N(d1) = 0.56946

Strike price: $40.00 N(d2) = 0.49003

Option maturity: 0.25

Variance of stock returns: 0.16

Risk-free rate: 6.0%

The Black-Scholes model calculates the value of the call option as:

V = P[N(d1)] – Xe^rt[N(d2)]

= $40(0.56946) – $40e^rt(0.49003)

= $22.78 – $19.31

= $3.47