I'm having o Windows 8 OS on my pc and Visual Studio 2013 Update 4 installed. Is it possible to develop apps on Windows Phone 8.1 in these conditions or an update to windows 8.1 is mandatory for this?
Windows phone 8.1 apps are two types - Silverlight and Windows runtime.
If you are building a Silverlight app, you can target your app to Windows Phone 8 and work on it.
However, only when you want to develop a
Universal App, you need Windows 8.1 since Windows Store apps, whether they run on phone / desktop have common runtime dependancies.