A shiny Pokemon's "worth" is quite questionable, honestly. It varies from person to person. For example, I would willingly part with things for a shiny Sandslash, because it has red spikes; but I would never do that for a shiny Heracross on this side of the grave, because it's pink. That's just one mentality, there are several others that might actually think the other way round.
Generally however, rarity-wise, a shiny Pokemon is worth way more than any ordinary Pokemon. It's like a trophy, even though it may not be very strong or good-looking, it's still something that most don't have and has weight in terms of "bragging rights". These days people can just use Power Saves and stuff to make their Pokemon shiny though, so the value has depreciated a lot.
As for trade, people do trade legendaries for shiny Pokemon. Same goes for other shinies. It really does depend upon the person; some don't even care if a Pokemon is shiny or not. You could trade your Shiny Mudkip for big stuff like other Shiny Pokemon or legendaries and have a good chance at succeeding. You could also sit back and wait for offers to come, which is also an option.
TL;DR: A Shiny Pokemon's worth is objective. Mostly however, they are worth much more than usual Pokemon
Hope I helped!