Some Pointers

1
Some Pointers

• Adjusting for dividends

2
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)

3
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).

4
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.

5
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.