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Why Unequal Replication Costs Create Arbitrage

Article Quant Q&A · Author: anthony
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Summary

The document explains the arbitrage argument behind a proof that forward and futures prices are equal under a constant interest rate. The proof compares two strategies that produce the same final capital. If their initial costs differ, an investor can take the more expensive side by selling it and buy the cheaper side, collecting the cost difference at the outset.

At maturity, the two positions offset because they deliver the same final amount, leaving no net payoff obligation. The initial proceeds therefore constitute a risk-free profit in the stated setup. This is a concise illustration of the law of one price and how replication supports no-arbitrage pricing. It does not provide the broader forward-versus-futures derivation or discuss assumptions such as financing, transaction costs, collateral, or changing interest rates; its argument applies to the matched strategies as described.

Key ideas

  • Strategies with identical final payoffs should have the same initial cost in a no-arbitrage market.
  • If one matched strategy costs more, an investor can sell it and buy the cheaper one.
  • The initial price difference is collected while the equal terminal payoffs cancel.
  • The example supports a no-arbitrage argument but does not establish all assumptions behind forward-futures price equality.

Tags

FuturesArbitrageDerivatives pricing
Full text
# If the interest rate is constant, then the forward price and the futures price are equal?


# If the interest rate is constant, then the forward price and the futures price are equal?












I was going through the proof about the equality of forward and futures price (assuming constant interest rate) in a book. Somewhere, the authors used the fact that suppose we start with two capitals - say A and B and we end up with the same final capital S, then A=B otherwise there will be arbitrage opportunity. Why arbitrage arises if A and B are not same?

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/72218

Say for example A>B. Then you would sell strategy A versus buying strategy B, collecting A-B initially. At the end you will have S-S, which is zero. So you have a risk free profit.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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