The frustum (near plane, far plane, fov) is in view space so multiplying it with an inverse view matrix will move it into world space. If you use DirectXMath (which I recommend) you can utilize the bounding frustum object. An example code might look something like this:
DirectX::BoundingFrustum frustum;
DirectX::BoundingFrustum::CreateFromMatrix(frustum, camera.getProjectionMatrix());
DirectX::XMMATRIX inverseViewMatrix = DirectX::XMMatrixInverse(nullptr, camera.getViewMatrix());
frustum.Transform(frustum, inverseViewMatrix);
BoundingFrustum docs: https://msdn.microsoft.com/en-us/library/windows/desktop/microsoft.directx_sdk.directxmath.boundingfrustum(v=vs.85).aspx
If your frustum is big and you have to view a large area (e.g. outdoor scene) then even a large moving shadow map might not be enough (or it takes a huge amount of memory). One technique to solve this is called cascaded shadow maps (CSM). In CSM more precise shadow maps are rendered close to the camera and less precise shadows are rendered in the distance where the low quality is not visible anyway. Here is a CSM tutorial in case you are interested: https://msdn.microsoft.com/en-us/library/windows/desktop/ee416307(v=vs.85).aspx