Assume $F_0$ is the delivery price of a forward contract on a commodity, say oil.

Let $S_0$ be the spot price and $U$ be the present value of all storage costs net income. Also let $r$ be the risk-free rate and $T$ time to maturity.

Let's say we have that $F_0 < (S_0 + U) e^{rT}$.

Hull (Options, Futures and Other Derivatives 10ed, pg 125) says if the asset was already held, an arbitrageur could:

  1. Sell the commodity, save on storage costs and invest the proceeds at the risk-free rate.
  2. Take a long position in the forward contract.

But what if the arbitrageur does not own the asset already? Can we still say there is an arbitrage opportunity here?


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