This may sound like a very dumb question. I’m new to options, and am creating a simple model to help me trade/learn the intricacies of options trading. One of the sections in the model simply uses the B&S formula to graph an options price change relative to changes in the underlying stock price. The question is, should this price change of the option (if graphed) be linear? ie: if the option is a $30 call, and the stock price goes steadily from $20 to $30 to $40 to $50, should the relative change in the option price be linear?
It should not. There is built in leverage for options. If the stock goes up 10%, the call option should move up more than 10%.