In the modern bow hold the index finger is placed on the stick just before the second knuckle. The thumb is placed opposite the middle finger.
What is the proper way to hold a violin bow?
Balance the bow between your shoulder and the right thumb tip. Keep your thumb bent down to the hair or the bow might roll away from you. Without upsetting the balance, lightly lower your fingers to the stick as the fingers fall naturally—the first three over, the pinkie tip on top.