  We prove the existence and pointwise lower and upper bounds for the
fundamental solution of the degenerate second order partial differential
equation related to Geman-Yor stochastic processes, that arise in models for
option pricing theory in finance.
  Lower bounds are obtained by using repeatedly an invariant Harnack inequality
and by solving an associated optimal control problem with quadratic cost. Upper
bounds are obtained by the fact that the optimal cost satisfies a specific
Hamilton-Jacobi-Bellman equation.
