is a surety bond required

Whether or not you need a bond depends on what the will requires.  If the will states you need a bond, then you do need a bond, if it say s you do not, then you do not.  The value of the estate doesn't necessarily control.  more importantly, if the outstanding amount of the mortgage exceeds the value of the house, you should not transfer the property at all, but instead allow the mortgage holder to do a deed in lieu of foreclosure, unless for some reason the beneficiary of the property wants the property notwhithstanding the mortgage.