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What is the Black-Scholes value for a dividend paying stock?

Question 1: 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 .
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?

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** Please see the attached file for complete details on how the numbers were calculated. **

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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.
B) Calculate the price of a 91-day European-style put option on ARB stock having the same exercise price.
The method for calculating the price of call option on a stock with dividends is similar to the method for calculating the price of call option on a stock without dividends.
The only difference in the case for stock with dividends is that we adjust the current stock price.
We will have to adjust the stock price S for the dividends to be received during the life of the option
For finding the adjusted price of the stock we subtract the present value of dividends to ...

Solution Summary

This solution calculates option value for a dividend paying stock using Black Scholes option valuation model.

$2.19