@stof is right. The documentation says that you must specify the time. But as @ddeboer noticed "It works !" From my experience I can tell you that NGINX's wiki is not always correct/updated.

If we want set the cache TTL from the application I suggest to *only* use http://wiki.nginx.org/X-accel#X-Accel-Expires (that is the variable with the higher priority) and forget about the others.