How to bake a cavity map from hi-poly to low-poly? Cavity Map Baking from Hi-Poly to Low-Poly

I have a hi-poly mesh object and a low-poly mesh object. The low-poly one is UV-mapped. I created a cavity map material in Cycles for the hi-poly object and I want to bake the color onto the low-poly object. The problem is that when I try this all the areas where the hi-poly mesh protrudes beyond the low-poly mesh get occluded and don't register in the bake.

Hi-poly and low-poly objects overlap like so:



And here is the problematic result:



My Cycles bake settings:



The material node setup of the low-poly object (bake target):



My Cycles cavity material (node setup and result on the hi-poly mesh):





One thing I tried without success was to enable double-sided normals in the Mesh Context options. Is there a better way to do this, or maybe some obvious solution I'm missing? Thanks in advance.

Update: Fixed!

Here is the result after applying lemon's answer, just to show for comparison:
This is a "symptom" of a need for 'ray distance' :



The bake casts rays around the meshes.
If parts of the mesh you want to bake to are too far from the highpoly mesh, the bake will miss them.

Hypothesis : as you use here an emission material that can involve problems for parts of the lowpoly that are inside (not lighted).