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11 September, 03:01

An analAn analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following dа ta: · 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?

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  1. 11 September, 03:20
    0
    Value of the call option using Black-Scholes Model is $3.47

    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
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Home » Business » An analAn analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following dа ta: · The price of the stock is $40. · The strike price of the option is $40.
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