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Value of Call Option using Black-Scholes model

A share of ARB stock sells for $75 and has a standard deviation of return equal to 20% per year. The current risk-free rate is 9% and the stock pays two dividends: 1) A $2 dividend just prior to the option's expiration day, which is 91 days from now (one quarter of a year) and 2) a $2 dividend 182 days from now.

A) Calculate the Black-Scholes value for a European-style call option with an exercise price of $70 (3 point).

B) Calculate the price of a 91-day European-style put option on ARB stock having the same exercise price.

C) How would a change in dividend policy impact the call option's value?

Solution Preview

Please see the attached file.

A share of ARB stock sells for $75 and has a standard deviation of return equal to 20% per year. The current risk-free rate is 9% and the stock pays two dividends: 1) a $2 dividend just prior to the option's expiration day, which is 91 days from now (one quarter of a year) and 2) a $2 dividend 182 days from now.

A) Calculate the Black-Scholes value for a European-style call option with an exercise price of $70.

The dividend that is received after the expiration date does not influence the price of the option.
Present value of dividends is subtracted from the current stock price before using the Black Scholes equation

risk free interest rate= 9%

Present Value of dividend= $2.00 received 91 days = 0.25 years from now

is equal to $1.9555 =2x e ^ (-0.09 x 0.25)

Current stock price= $75.00
Therefore, adjusted stock price= $73.0445 =75-1.9555

We will use Black Scholes Pricing Formula
Value of call= S N(d1) - X * e -r(T-t) * ...

Solution Summary

Calculates the value of call and put options using Black-Scholes model.

$2.19