The Heston stochastic volatility model has a boundary trace at zero volatility

We establish boundary regularity results in Holder spaces for the degenerate parabolic problem obtained from the Heston stochastic volatility model in Mathematical Finance set up in the spatial domain (upper half-plane) H = R x (0, infinity) subset of R-2. Starting with nonsmooth initial data u0 is an element of H, we take advantage of smoothing properties of the parabolic semigroup e(-tA) : H -> H, t is an element of R+, generated by the Heston model, to derive the smoothness of the solution u(t) = e(-tA)u(o) for all t > 0. The existence and uniqueness of a weak solution is obtained in a Hilbert space H = L-2(H; pi) with very weak growth restrictions at infinity and on the boundary partial derivative H = R x {0} subset of R-2 of the half-plane H. We investigate the influence of the boundary behavior of the initial data u(o) is an element of H on the boundary behavior of u(t) for t > 0.