# What happened to future price if rates become negative?

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? • 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). Sep 11 '19 at 22:06
• 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 ? Sep 11 '19 at 22:16
• Yes, it is theoretically possible, I don't see why not. Sep 11 '19 at 22:31
• 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, Sep 11 '19 at 23:26
• This is often known as a futures market in backwardation vs. contango. Sep 12 '19 at 7:05