Regularity of a Degenerate Parabolic Equation Appearing in Večeř’s Unified Pricing of Asian Options

Večeř derived a degenerate parabolic equation with a boundary condition characterizing the price of Asian options for both discrete and continuous arithmetic average. It is well understood that there exists a unique probabilistic solution to such a problem. However, due to degeneracy of the partial differential operator and lack of smoothness in the boundary data, the regularity of the probabilistic solution remained unclear in the case of discretely sampled Asian options. We prove the probabilistic solutions of Večeř’s equation associated with discretely sampled Asian options are regular solutions.