Relationship between the warrant price and the price of the underlying securityThe most important thing to remember is that the price of a call warrant tends to rise as the underlying security price rises and the price of a call tends to fall as the underlying security price falls. The price of a put tends to rise as the underlying security price falls and the price of a put tends to fall as the underlying security price rises.
So why buy a warrant and not the security? Because a warrant is leveraged. That means that for a given percentage change in the underlying price the option price can change by a greater percentage. You get a bigger bang for your buck.