Dividend Yield in Short Futures Contract Valuation

Summary

The document presents cost-of-carry relationships for pricing a forward on an asset that pays dividends or another yield. It gives equivalent expressions using a continuous yield or the present value of future cash flows, then states the value formula for a long futures-style contract and asks how to value the short side, especially with respect to dividends.

Its useful starting point is the distinction between the forward price and the contract’s value: the long position’s value is the present value of the underlying adjusted for yield, less the discounted delivery price. The short position follows by reversing the sign of that long value, so the dividend adjustment changes direction with the position. The document itself contains no answer, worked example, or discussion of contract settlement conventions. Its formulas therefore serve as a setup for the question rather than a full treatment of futures pricing or dividends.

Key ideas

• The forward price incorporates the underlying’s dividend yield through cost of carry.
• The present value of future cash flows can express the same adjustment as a continuous yield.
• The stated long contract value compares the yield-adjusted underlying with the discounted delivery price.
• A short position has the opposite value of the corresponding long position under the same assumptions.

Tags

# Valueing a Short future contract with dividens


# Valueing a Short future contract with dividens












A forward of an underlying paying a yield $q$ can be priced with the equation:

Price $= S_0 e^{(r-q)*t}$

or

Price $= (S_0-I)e^{rt}$

Where $S_0$ = Spot price, r = interest, q = dividend yield, I = PV of future cash flows and t = time.

The value of a long future contract would be:

Value $= S_0 e^{-q t} - Ke^{-rt}$

or

$S_0 - I - Ke^{-rt}$.

My question is how the value would differ if it were a short future contract, specifically i'm wondering regarding the dividends.

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