Hotmail stores your data locally on your PC in an ".OST" (not ".PST" ) file. You could create backup copy of your OST file, but (as far as I know, unlike PST files) there is no way easy way to restore an OST file to Outlook.
If you want to backup Hotmail account, you can do so by exporting your Hotmail account to a PST file. You can choose to backup your entire Hotmail account, or you can just backup your contacts or calendar, etc. The instructions for doing exporting to a PST file vary depending on your version of Outlook. You can easily find instructions online. For Outlook 2010, it's under "File/Open/Import/Export to a File/Outlook Data File (.pst)".