One of my simulation tends to converge to several thousands volts or negative voltage before totally give up.

If there is a knob to set the max and min allowed value during initial condition convergence, that may help simulator to converge.

Is there such knob available in hspice?

I have also seen this kind of behaviour caused by poor Verilog A models. For example, I have seen a few cases where people model non-linear resistance with a quadratic (or higher order) equation, neglecting the fact that quadratic equations have multiple roots. If those roots represent completely non-physical behaviour, the simulator doesn't know that - so it may be a "correct" solution to have large negative voltages if the model is not reasonable...

Regards,

Andrew.