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Dividends and Option Pricing

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.

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Dividends and Option Pricing

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  1. 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)

  2. An Example • Suppose you were valuing an option on the stock of Target as of 15 November 2004. The maturity of the option is 19 November 2004. • 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).

  3. 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.

  4. 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.

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