I am trying to understand the stochastic model of a financial market in one period by [Föllmer, Schied]. They introduce call and put options for the primary assets, which are non-negative. They do not specify if the strike can be negative or if it should be positive. I think its economically not useful to have negative strike prices for options whose underyling is one of the primary assets. Since $(S -K)^+>0$ for $S\ge 0$ and $K<0$ it would be basically a sure payoff. Is this a fair assessment?
Next, they define basket options, whose underyling is the value of some portfolio. Some portfolio can have negative inital value. Thus, I believe that it could be useful to have a negative strike price. Is this true?
Wikipedia page on strike prices does not specify it either.
I can specify the model if necessary. Let me know. Thanks for reading.