Go to Settings > Notifications > Stock Widget and turn it Off.
You'll see two lists ofNotifications for all apps that can display them are managed in (it takes a moment to populate)Settings.
From here you can turn off Two built-in apps, Stocks and on notifications for any appWeather, get exceptional treatment and show in Notification Center as widgets. In the Notifications Settings, they are listed as Stock Widget and the Weather Widget.
To prevent an app (i.e. Stocks) from displaying in Notification Center, click the app in the list and make sure the option “Notification Center” is set to off.