18.2 Continuous Dividend

Problem. Amazon.com doesn't pay a dividend, but suppose that it did. Specifically, suppose that

Amazon.com paid dividends in tiny amounts on a continuous basis throughout the year at a 3.00% / year

rate. What would be the new price of the April 100 European call and April 100 European put?

Solution Strategy. Modify the Basics spreadsheet to incorporate the continuous dividend version of the

Black Scholes model.

FIGURE 18.2 Spreadsheet for Black Scholes Option Pricing - Continuous Dividend.

How To Build This Spreadsheet Model.

1. Start with the Basics Spreadsheet, Add A Row, and Enter The Dividend Yield. Open the

spreadsheet that you created for Black Scholes Option Pricing – Basics and immediately save the

spreadsheet under a new name using the File | Save As command. Add a row by selecting the

cell A9 and clicking on Insert | Rows. Enter the dividend yield in cell A9.

2. Modify the d1 Formula. In the continuous dividend version, the 1 d formula is modified by

subtracting the continuous dividend yield d in the numerator. The new 1 d formula is

ln / 2 / 2/ RF P X k −d ⋅t ⋅t . In cell B12, enter

=(LN(B4/B7)+(B6-B9+B5^2/2)*B8)/(B5*SQRT(B8))

3. Modify the Call Price Formula. The modified call formula is

1 2

V Pe−dtN d −Xe−kRFtN d , where d is the continuous dividend yield. In cell B16, enter

=B4*EXP(-B9*B8)*B14-B7*EXP(-B6*B8)*B15

We see that the Black-Scholes Option Pricing - Continuous Dividend model predicts an European

call price of $21.91. This is a drop of 69 cents from the no dividend version. Now let's do the put.

4. Modify the Put Price Formula. The modified put formula is

1 2

Put −Pe−dtN −d Xe−kRFtN −d . In cell B22, enter

=-B4*EXP(-B9*B8)*B20+B7*EXP(-B6*B8)*B21

We see that the Black-Scholes model predicts an European put price of $18.57. This is a rise of 40 cents

from the no dividend version.

Problem. Amazon.com doesn't pay a dividend, but suppose that it did. Specifically, suppose that

Amazon.com paid dividends in tiny amounts on a continuous basis throughout the year at a 3.00% / year

rate. What would be the new price of the April 100 European call and April 100 European put?

Solution Strategy. Modify the Basics spreadsheet to incorporate the continuous dividend version of the

Black Scholes model.

FIGURE 18.2 Spreadsheet for Black Scholes Option Pricing - Continuous Dividend.

How To Build This Spreadsheet Model.

1. Start with the Basics Spreadsheet, Add A Row, and Enter The Dividend Yield. Open the

spreadsheet that you created for Black Scholes Option Pricing – Basics and immediately save the

spreadsheet under a new name using the File | Save As command. Add a row by selecting the

cell A9 and clicking on Insert | Rows. Enter the dividend yield in cell A9.

2. Modify the d1 Formula. In the continuous dividend version, the 1 d formula is modified by

subtracting the continuous dividend yield d in the numerator. The new 1 d formula is

ln / 2 / 2/ RF P X k −d ⋅t ⋅t . In cell B12, enter

=(LN(B4/B7)+(B6-B9+B5^2/2)*B8)/(B5*SQRT(B8))

3. Modify the Call Price Formula. The modified call formula is

1 2

V Pe−dtN d −Xe−kRFtN d , where d is the continuous dividend yield. In cell B16, enter

=B4*EXP(-B9*B8)*B14-B7*EXP(-B6*B8)*B15

We see that the Black-Scholes Option Pricing - Continuous Dividend model predicts an European

call price of $21.91. This is a drop of 69 cents from the no dividend version. Now let's do the put.

4. Modify the Put Price Formula. The modified put formula is

1 2

Put −Pe−dtN −d Xe−kRFtN −d . In cell B22, enter

=-B4*EXP(-B9*B8)*B20+B7*EXP(-B6*B8)*B21

We see that the Black-Scholes model predicts an European put price of $18.57. This is a rise of 40 cents

from the no dividend version.