Yes, you need a SSL Certificate to send traffic via HTTPS. Some hosts provide a wildcard SSL Certificate so you can use the HTTPS protocol, but users might get errors saying the certificate’s not issued to there domain.
You need an SSL certificate to verify that the client is communicating with a trusted party (the server), and to issue digital certificates and public/private keys transfers and verifications.
But you do need a Certificate. Some web hosts (Shared Hosting) also charge an installation fee to install SSL Certificates.
The following articles may help you:
Once you have installed your SSL Certificate, check out SSL Shopper to validate the installation