The Pricing of Asian Options in Uncertain Volatility Model

This paper studies the pricing of Asian options when the volatility of the underlying asset is uncertain. We use the nonlinear Feynman-Kac formula in the G-expectation theory to get the two-dimensional nonlinear PDEs. For the arithmetic average fixed strike Asian options, the nonlinear PDEs can be transferred to linear PDEs. For the arithmetic average floating strike Asian options, we use a dimension reduction technique to transfer the two-dimensional nonlinear PDEs to one-dimensional nonlinear PDEs. Then we introduce the applicable numerical computation methods for these two classes of PDEs and analyze the performance of the numerical algorithms.