At least with things like OwnCloud[1] you get to actually own your data instead of having it on a SaaS/PaaS Cloud. The cloud is just someone elses computer.
I know it's 'free', but Protonmail[1] does look promising. Not sure it has a calendar app though. I think Mailbox.org[2] has some office features like a calendar. The basic plan on Mailbox is EUR1.00 per month, but they do have other plans if you need more storage.