Java Swing使用ButtonGroup数组报错

import javax.swing.*;

public class test {
    public static void main(String[] args) {
        JFrame frame = new JFrame("test");
        ButtonGroup[] options = new ButtonGroup[3];
        for (int i = 0; i < options.length; i++) {
            JRadioButton button = new JRadioButton();
            options[i].add(button);
            frame.add(button);
        }
        frame.pack();
        frame.setVisible(true);
    }
}

报错如下

Exception in thread "main" java.lang.NullPointerException
    at Swing.component.test.main(test.java:11)

为什么会报错？为什么使用ButtonGroup数组就会报NullPointerException的错？