Deep:

"that's the point"?!

What point?

We aren't talking about the share price acting as an option on the share price, you know.

We should be comparing the derivative (option) payoff functions on the underlying items.

The underlying item on a regular option is the share price.

The underlying item on the SSO share price is the price of silver.  (or at least, that is the thesis)

We shoud be comparing:

a) The payoff function of a "generic option" as a function of the price of the "generic underlying item"

b) The payoff function of SSO as a function of the price of the underlying item (the price of silver)

To whatever extent function a) is like function b), then to that extent SSO share price is like a never expiring option on silver. 

What possible connection does the identity function play in this discussion?

I'll take your word on a "perpetual" option having a convex function curve.  It is plausible.  Never having seen such a beast myself I cannot claim to be an expert on such.  I still think that this little tidbit of information has little to no bearing on the real point of this discussion.   (see next response post)