Dividends
Another difference between call and married-put values is dividends. A call
option does not extend to its owner the right to receive a dividend payment.
Traders, however, who are long a put and long stock are entitled to a
dividend if it is the corporation’s policy to distribute dividends to its
shareholders.
An adjustment must be made to the put-call parity to account for the
possibility of a dividend payment. The equation must be adjusted to account
for the absence of dividends paid to call holders. For a dividend-paying
stock, the put-call parity states
The interest advantage and dividend disadvantage of owning a call is
removed from the market by arbitrageurs. Ultimately, that is what is
expressed in the put-call parity. It’s a way to measure the point at which the
arbitrage opportunity ceases to exist. When interest and dividends are
factored in, a long call is an equal position to a long put paired with long
stock. In options nomenclature, a long put with long stock is a synthetic
long call. Algebraically rearranging the above equation:
The interest and dividend variables in this equation are often referred to
as the basis. From this equation, other synthetic relationships can be
algebraically derived, like the synthetic long put.
A synthetic long put is created by buying a call and selling (short) stock.
The at-expiration diagrams in Exhibit 6.2 show identical payouts for these
two trades.