Unfortunately, you can’t add your name to your grandfather’s policy unless you live with him. Insurance companies look at the location where the car is kept and the specific city you live in to determine your premiums. Also, if the car is registered in your name, your grandfather can’t insure it. It would be best to stay on your own policy.
To lower your car insurance payments, try looking into a multi-policy discount, increasing your deductible, or taking any defensive driving courses available in your state.