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Imagine the spot price of a non deliverable and not paying dividend asset is 100\$. With positive rate, the theoretical formula $F = S \cdot e^{rT}$ give us a future price higher, let's say 105.

If rate become negative before maturity, does the future price will 'cross' the spot price of the underlying asset? Because with negative $r$, $F$ will be reduce and could be lower than $S$, so at some point will there be a 'cross' of the two prices?

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    $\begingroup$ Yes, $\exp(rT)$ is $>,=,<1$ according to whether $rT$ is $>,=,<0$. And by assumption $T\ge 0$. So the sign of $r$ is what matters for the relationship between $F$ and $S$. But there is nothing wrong or unusual with $F<S$, it has happened before in the markets for reasons which are not included in this simple equation (things like dividends and convenience yield, discussed in more advanced models). $\endgroup$
    – Alex C
    Sep 11 '19 at 22:06
  • $\begingroup$ Yes but my question is more precisely on one contract, if for example in march, spot is 100 and june future contract is 107, and in may rates become negative, does the june future contract price can go down for example at 97 and spot be still at 100 ? $\endgroup$
    – TmSmth
    Sep 11 '19 at 22:16
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    $\begingroup$ Yes, it is theoretically possible, I don't see why not. $\endgroup$
    – Alex C
    Sep 11 '19 at 22:31
  • $\begingroup$ If r>0, then the forward price will be lower than spot! And versa, if r<0, then forwards become larger than spot. Money just went from backwardation into contango. No different to crude oil, no magic required, $\endgroup$
    – demully
    Sep 11 '19 at 23:26
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    $\begingroup$ This is often known as a futures market in backwardation vs. contango. $\endgroup$
    – Quantuple
    Sep 12 '19 at 7:05
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Futures actually have a negative basis all the time without having to have negative interest rates. Dividends can have a rate that is higher than the interest rate and that makes the basis negative. Futures on the Dow Jones Real Estate Index are almost always negative.

Here are the DJUSRE Sep and Dec futures. The "Spread" column shows you the negative basis:

DJUSRE Index FAIR

As dividends go ex and repo rates change the basis can, and does, swing form positive to negative to positive and all over again. Here is the basis for the SP500, a little niche index you might have heard of:

enter image description here

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  • $\begingroup$ Yes i'm aware that i could be lower than the spot, my question was more could it switch during the life of the same contract, like this : imgur.com/a/lOZgFyI $\endgroup$
    – TmSmth
    Sep 12 '19 at 17:14
  • $\begingroup$ Yes, happens all the time. I'll enhance my response to show you. $\endgroup$
    – JoshK
    Sep 12 '19 at 17:16
  • $\begingroup$ Did my answer make sense? $\endgroup$
    – JoshK
    Sep 13 '19 at 0:10
  • $\begingroup$ Yes thanks that's a concrete example $\endgroup$
    – TmSmth
    Sep 13 '19 at 16:13

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