In this paper we continue to study a non-local free boundary problem arising in financial
bubbles. We focus on the parabolic counterpart of the bubble problem and suggest
an iterative algorithm which consists of a sequence of parabolic obstacle problems at each
step to be solved, that in turn gives the next obstacle function in the iteration. The convergence
of the proposed algorithm is proved. Moreover, we consider the finite difference
scheme for this algorithm and obtain its convergence. At the end of the paper we present
and discuss computational results.