Upper bound put option with and negative underlying price

[yoneda]

Hi guys, I know this is very basic but can someone confirm the following? Say I have a put option on some underlying which could trade at a minimum -s for s >=0. Then an American put must satisfy P < (K+s). As you can see this is clearly inspired from the negative oil futures incidence. Many thanks!

[deeds]

One model to look at this with sensible assumptions is matching three moments to provide shifted lognormal (a lot of literature in option pricing on baskets and spreads on this)...kind of next simplest model after black scholes (open to debate)



EDIT: this approach allows price process which can go negative

[ronin]

Strictly speaking, K+s discounted. K+s is the bound on payout, not price.



Because, if funding rates are negative too, then K+s discounted > K+s.



You know, there was a time when I thought that asking or answering questions like this was just intellectual masturbation. Good old days.