Valuation Differences Between MSR and IO

Hey guys!

I’m needing to get a handle on the valuation of MSRs. On the surface, I’d think they’d behave like IOs in value in the sense that as rates begin to rise, the value will rise as prepayments slow. But as rates continue to rise, the value then begins to fall because prepayments aren’t slowing at any material rate, but the discount rate is increasing. However, thing that MSRs can have that IOs don’t is the float associated with the payments held for remittance. I’m having trouble finding stuff on the internet about this, so was curious if any of the BSDs had much experience in this area.