Role of next month's dividends in forward pricing

Question

I'm using the equations given on this page to price forwards on an equity.

It's a basic equation that discounts dividends.

But my question is: What do we do about dividends that occur after the forward's expiration date?

For example, consider a stock that pays dividends on the last day of every month in the year. Say I want to price the forward that expires on the 15th of March. According to that webpage, I only need to discount dividends paid on January 1st, February 1st, and March 1st. But what about the dividend that will be paid on April 1st. On March 15th, we would be halfway through the month and the stock will have accrued half of the value of the next dividend. So how should I treat months after the forward? Thanks.

Answer 1

A long equity forward position initiated at $t=0$ for delivery at $T$ can be replicated by borrowing cash to purchase the stock at $t=0$, carrying that stock up to $T$ and paying the interests on the cash borrowed (cash & carry). This shows that the forward price is basically the cost of funding the equity purchase.

Now if the stock pays dividends the proceeds can be reinvested, which contributes to decreasing the effective funding cost. Obviously only the dividends falling over the replication period $]0,T]$ can be reinvested and hence matter in pricing the forward $F(0,T)$.

In practice there is an additional complication due to the 'ex-dividend' date versus 'payment' date discrepancy but the idea remains the same.