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The relationship between an option's price and the price of the underlying stock or futures contract is called its delta.
If the delta is 1, for example, the relationship of the prices is 1 to 1. That means there's a $1 change in the option price for every $1 change in the price of the underlying instrument.
With a call option, an increase in the price of an underlying instrument typically results in an increase in the price of the option. An increase in a put option's price is usually triggered by a decrease in the price of the underlying instrument, since investors buy put options expecting its price to fall.