There is a species of (tropical?) tree of the Genus Bucida that is a common tree often called olive or olive oak that is no relation to actual olives and a distant relative of oaks that it resembles but does not lose its leaves. I have never seen it as wood but would expect it to be similar (cut branches are light like oak)
Actual Olive wood is available and looking I see @evansd2 was the one who pointed it out.
I have not tried cutting it yet but it is very beautiful 
I am glad to hear it will not burst into flames but I have not yet come up with a design that deserves it. It is supposed to come from ancient olive trees and from what we know about what is happening there the must be quite a lot of such wood about.