How to set a refresh rate in a Subscribed Calendar

As of 2019/iOS 12.3.1, these settings are under Passwords and Accounts → Fetch New Data → Fetch. It looks like fetch settings are applied globally to all fetch accounts - you can't set different fetch options for individual calendars or mail accounts.

In "Settings->Mail, Contacts, Calendars->Fetch New Data" you can setup what to do. Depending on the account you can Fetch or Push updates to your iPhone - or choose to do it manually.

When viewing Calendar, click on Calendars button in top left. Down at bottom left corner you'll see the refresh circular arrow. Click it and it will refresh all subscribed calendars.