Before revision: We study the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space.
After revision: We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space.