DIVIDENDS AND THEIR EFFECT ON OPTIONS
Although dividends are not the first concern of an option trader it is important to understand how they affect option pricing. In this section this will be explained and the reader will be introduced to forwards.
Forwards are agreements to buy or sell shares at a future point in time without having to make a payment up front. Unlike an option, the buyer of a forward does not have an option at expiry. For example, the buyer of a 6-month forward in Royal Dutch/Shell commits himself to buying shares in Royal Dutch/Shell at a preagreed price determined by the forward contract. The natural question is, of course: What should this preagreed price be? Just like Black and Scholes did for the pricing of an option the price is determined by how much it will cost to hedge the forward position. To show this, consider the following example. An investment bank sells a 2-year forward on Royal Dutch/Shell to an investor. Suppose that the stock is trading at $40, the interest rate is 5% per year and after 1 year Royal Dutch/Shell will pay a dividend of $1. Because the bank sells the forward it commits itself to selling a Royal Dutch/Shell share in 2 years’ time. The bank will hedge itself by buying a Royal Dutch/Shell share today. By buying a Royal Dutch/Shell share the bank pays $40, over which it will pay interest for the next 2 years. However, since the bank is long a Royal Dutch/Shell share it will receive a dividend of $1 ...