I recently spoke to an options trader that tried to demonstrate option pricing by considering a random walk of balls dropping down a lattice so the underlying stochastic process is a simple random walk of say 100 steps.
The contract considered is $(U_{100}-K)^{+}$ where $U_{100}$ is the number of times the ball goes "up". He states that this is an option. I think he doesn't understand what an option is because there is no underlying market in this case (ie you can't exactly trade the balls to hedge your position and there is no underlying that moves based on what the ball does except for the contract itself). I would say that this is a bet or a game that you would pay for at a casino.
So my question is: Is there a resource that actively explains or demonstrates why a derivative is called a derivative? As in why insurance and bets are fundamentally different from derivatives?