I am revamping a current website that was initially designed as asp; however, the site has only 10 pages total. All are static pages with no asp coding...yet all the pages are saved as .asp. My question is, what is the advantage of .asp over .htm if the pages are static?

There is none. ASP is a server side scripting language, it allows you more interaction with your visitors, it is similar to PHP.

If your pages contain no ASP scripting (found between <% %> tags) then it is semantically incorrect to use the extension .asp. If they are static HTML pages (with no ASP inside) simply have them as .html

You can't compare ASP and HTML because they are two different things. HTML often contains ASP within it, and ASP can be used to generate HTML.

If your pages contain no ASP scripting (found between <% %> tags) then it is semantically incorrect to use the extension .asp.

Nope. it doesn't matter whether a page with a .asp extension contains any asp code or not. There's no "semantically correct" reason to use any extension.
If you want to have .asp pages with no asp code you can.

If they are static HTML pages (with no ASP inside) simply have them as .html

Nope leave them as .asp it will save grief and extra work if at some point you need scripting on them.

Actually, there is a use for ASP that contains no ASP coding: server-side include layout files.

Theoretically, you could see something along the lines of

<!--#include file="header.asp"-->
Body code.
<!--#include file="footer.asp"-->

Which would work fine, have no timestops and allow for quick and easy layout changes. Mind you, the pages could have also been created in .SHTML (assuming the server supports it...I suppose there COULD be a case where it isn't and ASP is, but that's very unlikely.)

I would suggest that the idea of separating layout from content would be the most likely reason ASP was used if no scripting was involved, and that's something plain ol' HTML just won't do.

It won't hurt anything to leave it the way it is, as chrishirst pointed out. If it ain't broke, don't mess with it.