Some Pointers Adjusting for dividends

Dividends and Option Pricing The buyer or seller of an option trades the ex-dividend stock. Thus, when we value an option, we have to adjust the market price of the stock (which I cum-dividends) by subtracting out any dividends that are to be paid over the maturity of the option. Ex-dividend stock price = cum-dividend stock price – PV(dividends)

An Example Suppose you were valuing an option on the stock of Target as of 15 November The maturity of the option is 19 November You check the company website, and find that the Target stock goes ex-dividend on 11/18/2004. The dividend amount is $0.08. Because the ex-dividend date is between 11/15/2004 and 11/19/2004, you have to subtract the dividend from the price. If the market price of Target is 52.43, the ex- dividend price is (52.43 – 0.08 = $51.35).

Index Option and Dividends It is difficult to get a complete accounting of the dividends for an index. Instead, we can approximately compute the ex- dividend index price by assuming that dividends are paid evenly over time. Thus, if we know the total annual dividend, then: Ex-dividend index price = Cum-dividend index price x exp( - d T), where d = dividend yield, and T= maturity of the option.

Using the Black Scholes formula Most implementations of the Black-Scholes formula allow for a dividend yield. So when you value an option on an index, you simply substitute the market index level, and the dividend yield into the formula. On the other hand, if you want to use the same formula to value an option on a stock, you put the dividend yield equal to 0, and use the ex-dividend stock price that you computed earlier.