Basically the subject says it all.
We have SharePoint 2013. We only have site collection access.
Has anyone have a solution where a calendar from a sub-site can be displayed on the Home page that the sub-site falls under.
You can use Calendar overlay if you have not tried this option. please follow the instructions below.
On the home site collection click on the calendar list and then select the "Calendar Overlay" option from the top ribbon bar.
On the next screen, follow the instructions as shown in the picture below in sequence.
Now, when you go back to your calendar in the site collection, you will notice the calendar name of the subsite is displayed in the left navigation bar(ref pic below).
There is just one dependency, i.e. to create the calendar on site collection also. If you are okay with that you can use this option.
You can use the Page Viewer webpart and set the link to page as follow: Suppose the URL of your calendar looks like https://server/sitecollection/subsite/Lists/Calendrier/calendar.aspx
add the parameter ?isdlg=1 to the end of the URL to get: https://server/sitecollection/subsite/Lists/Calendrier/calendar.aspx?isdlg=1
and then set this URL to the webpart. Also, notice that the height of the webpart will not adapt to the content of the page, modify the height of the webpart to something like 800px to fix this.