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Pricing Index Futures with Multiple Dividend Payments

Article Quant Q&A · Author: 1190
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Summary

The document asks how to find the fair value of a three-month futures contract on a two-stock index when each stock pays a dividend before expiry. The answer gives the cost-of-carry approach: express financing costs and expected dividends in index points, then adjust the spot index value for both over the contract’s life. The single-stock formula must account for each dividend at its payment time; the index’s aggregate dividend contribution is what matters for the futures price.

The example specifies stock prices, dividend amounts and dates, an index value, and a monthly financing rate, but it does not work through the numerical calculation. It points to an external reference for further explanation. The response also does not detail how the two stock prices map into index points, so the index’s construction and dividend weights would be needed to calculate a specific fair value. The discussion provides a conceptual hint rather than a complete derivation.

Key ideas

  • Index futures value reflects spot value, financing costs, and dividends expected before expiry.
  • Convert each constituent’s dividend into its contribution to the index before combining payments.
  • Account for the timing of each dividend and the contract’s financing convention.
  • The example does not provide enough index-weighting detail to complete a numerical valuation.

Tags

FuturesEquitiesCarryDerivatives pricing
Full text
# calculation of theoretical value of futures contract


# calculation of theoretical value of futures contract












we form a stock index by using only two stocks in the index.

One of the stocks is the Stock-A. The current selling price of the stock-A is 103 dollars and the second stock is the stock-B. The current selling price of the stock-B is 56 dollars.

The current value of the index is equal to 267 dollars. Stock-A pays a dividend of 13 dollars in 1 months.

Stock-B pays a dividend of 1.3 dollars in 2 months.

We form a futures contract written on this index expires in 3 months.

Currently, the finance cost of carry in the market is 0.42% per month.

How can we calculate the futures contract's theoretically fair value which is monthly compounding.

Should I use the formula $f(T)= S_{stock}(1+r)^T-D_T$ ?

I don't understand how can I use this formula when for two dividend payments and two different stocks exist?

Can you please give me a hint to solve this question?

## Answer by marain (score 1)

https://quant.stackexchange.com/a/54275

$$ Futures Price = Spot Index Value + Finance Charges - Dividends $$ You need to convert everything into index points. Check this out: https://www.cmegroup.com/education/files/understanding-stock-index-futures.pdf

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.