# 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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#### Solution Preview

** 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.