Dividends and Option Pricing
The preceding discussion demonstrated how dividends affect stock traders.
There’s one problem: we’re option traders! Option holders or writers do not
receive or pay dividends, but that doesn’t mean dividends aren’t relevant to
the pricing of these securities. Observe the behavior of a conversion or a
reversal before and after an ex-dividend date. Assuming the stock opens
unchanged on the ex-date, the relationship of the price of the synthetic stock
to the actual stock price will change. Let’s look at an example to explore
why.
At the close on the day before the ex-date of a stock paying a $0.25
dividend, a trader has an at-the-money (ATM) conversion. The stock is
trading right at $50 per share. The 50 puts are worth 2.34, and the 50 calls
are worth 2.48. Before the ex-date, the trader is
Long 100 shares at $50
Long one 50 put at 2.34
Short one 50 call at 2.48
Here, the trader is long the stock at $50 and short stock synthetically at
$50.14—50 + (2.48 − 2.34). The trader is synthetically short $0.14 over the
price at which he is long the stock.
Assume that the next morning the stock opens unchanged. Since this is
the ex-date, that means the stock opens at $49.75—$0.25 lower than the
previous day’s close. The theoretical values of the options will change very
little. The options will be something like 2.32 for the put and 2.46 for the
call.
After the ex-date, the trader is
Long 100 shares at $49.75
Long one 50 put at 2.32
Short one 50 call at 2.46
Each option is two cents lower. Why? The change in the option prices is
due to theta. In this case, it’s $0.02 for each option. The synthetic stock is
still short from an effective price of $50.14. With the stock at $49.75, the