Pricing an Index Futures Contract with Dividends and Monthly Carry

Summary

The document addresses how to calculate fair value for a futures contract on a two-stock index when the component stocks pay dividends before expiry. The central issue is that the index level is expressed in index points, so dividends stated as currency amounts per share cannot be subtracted directly from it. They must first be converted into index points using the index divisor.

After converting the cash dividends, the cost-of-carry calculation can account for their different payment dates by carrying each dividend forward to expiry from its payment date, while carrying the spot index value over the full contract term. The question gives an example with monthly compounding and staggered dividends, but the response only clarifies the units conversion; it does not provide a worked numerical answer or discuss index construction details beyond the divisor. The method therefore depends on knowing the index divisor and applying consistent timing and compounding conventions.

Key ideas

• Index futures pricing must use quantities expressed in the same units as the index level.
• Convert per-share cash dividends into index points using the index divisor before including them in carry calculations.
• Each dividend is carried from its payment date to futures expiry, while the spot index is carried over the full term.
• The calculation relies on the divisor and consistent assumptions about dividend timing and compounding.

Tags

# Calculating the theoretically fair value of this futures contract by assuming monthly compounding


# Calculating the theoretically fair value of this futures contract by assuming monthly compounding












I need a help for the following question:

A stock index is constructed by including only two stocks in the index. One of the stocks (Stock $1$) currently sells for $250$ dollar and the other stock (Stock $2$) sells for $187.5$. The current value of the index is $437.5$. Stock $1$ is expected to pay a dividend of $7.5$ in one months and Stock $2$ is expected to pay a dividend of $2.5$ in two months. A futures contract written on this index expires in three months. Currently, the finance cost of carry in the market is $0.75%$ per month. Calculate the theoretically fair value of this futures contract by assuming monthly compounding.

Here what i have done so far: $f_0(T)=437.5(1.0075)^{3/12}-7.5(1.0075)^{2/12}-2.5(1.0075)^{1/12}$ I think this is not true. Where do i make mistake? Should i use stock $1$ and stock $2$?

## Answer by JazKaz (score 1)

https://quant.stackexchange.com/a/54373

You must convert all cash and dividend streams into the index points . The current value of the index between stocks seems ok but the dividends need to be converted to index points.

Basically divide the dividends you’ve calculated by the index divisor. Then the calculation seems ok

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