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

question 4

Multiple Choice

An 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?

• A) $2.81
• B) $3.12
• C) $3.47
• D) $3.82
• E) $4.20

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Definitions:

Total Percentage Return

The total return on an investment, including both capital gains and dividends, expressed as a percentage of the initial investment.

Dividends

Distributions of earnings from a corporation to its owners, sharing a part of the company's income.

Shares

Equity shares in a corporation or financial asset, offering stakeholders a balanced share in the declared profits through dividends.

Average Rate

Typically refers to the mean rate or typical value for a given measure over a set time period or dataset.