Can it have a value different from 0 ?I suppose that if the forward price of the underlying is negative, then yes (for example, a stock at 1$, with a huge repo and a huge dividend : it surely never happened but it is possible or negative forward rates ; did it happen in the past by the way ?). But this assumes that I delta-hedge. If I sell a put with strike 0, then I won't hedge it since it is never going to be in the money. So its value is 0. But if I hedge it with the underlying, and that this underlying has a negative forward price, the put should have a value different from 0. Am I right ? And if there any risk selling this put for virtually nothing if I don't hedge it (of course, I would not do it in practice, just in case...) ?Thanks

Sorry for the stock, it was just an example for a negative forward price. But what for interest rates ? I thought that in asia and in france some time ago, forward rates were negative. What happened in that case ? Did the put have a value different from 0 ? If I want to make a bet on the fact that forward rates will become negative, how do I cash in the money, knowing that at expiry, my put will be OTM ?

A week ago a 20Y10Y receiver 0% strike traded for 2 ticks.In yards.Regards,Cactus