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Is it possible to make an arbitrage profit by taking a long position in the futures contract and a short position in the forward contract when Forward Contract F(0,0) > Futures Contract G(0,0)? That is, the forward contract and futures contract at time = 0 and state = 0.

I believe it has to do with the fact that under the No-Arbitrage Axiom, we must have that F(N,j) = S(N,j) (foward price equal to asset price) and G(N,j) = S(N,j) (futures price equal to asset price) when the interest rates are deterministic, but what if it isn't?

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  • $\begingroup$ Are you prepared to trade forwards OTC to make the trade? In theory, futures and forwards are equivalent at expiry, but there are lots of reasons there could be deviations in the interim. This isn't really an arbitrage opportunity, and even if it is, it's obvious enough that you're competing with a dozen desks that already have infrastructure set up to scrape it $\endgroup$
    – Chris
    Oct 24, 2020 at 8:19

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Forwards and futures only need to agree on price in a world with deterministic interest rates as a general rule (it is possible to cook up examples of random rate models where the correlation between the underlying and the rate process force the same relationship but they are rather contrived). That covers the general case but your questions revolves around the expiry process and that can be different even if rates are deterministic due to market microstructure issues. For example, the forward may be physically settled while the future is cash settled. This would allow a basis to continue into expiry as anyone trying to arbitrage it would be forced to open and close spot positions at a cost to themselves.

In general arbitrage conditions puts bounds on price processes, so there is some range that a forward and future need to coincide in at expiry but it is only a single point in idealized mathematical models.

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  • $\begingroup$ I see. So there is a a possibility to make an arbitrage profit? $\endgroup$
    – UnevenMango
    Oct 23, 2020 at 21:23
  • $\begingroup$ Is this because if the interest rates are non-deterministic, theres lost opportunity for the futures contract. That is, because there is an exchange that takes money out of the margin account, if we spend time in the losing position, our lost interest from the futures could wipe out the arbitrage profit? $\endgroup$
    – UnevenMango
    Oct 23, 2020 at 21:24

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