Deep,

Perhaps the asymmetric payoff and the non-negative second derivative are caused by the fact that options have an expiry date and are therefore not entirely composed of intrinsic value?

Therefore, if we had such a mythical beast as a "non-expiring" option, it might well have a symmetrical payoff function with respect to the underlying item.

(or not, who would really know?) 

BTW   I think you made a little goof...  *Everything* is linear with respect to itself.  Perhaps you meant that the stock price of SSRI is linear with respect to the price of silver?  That would have better correlation to the content of the conversation.  I am not sure that is exactly true, however.

I suspect that once the price of silver dropped below the cost of SSRI mining it that the function might become decidedly non-linear!

It would probably have dropped relatively close to the "resale value" of non-resource assets of the company and would vary at a much lower leverage after that.

i.e.  the function would show a clear inflection point. 

Regardless, I think to most people - who are not "one of the foremost Metals option experts" - the fact that one is positively correlated to the other and with leverage is sufficient similarity to justify the statement.

Most would not be concerned with the asymmetry in the payoff function, and would write it off as a minor point of difference not sufficient to negate the original comparison.

 Just my opinion, of course.