Knightian Uncertainty Based Option Pricing with Jump Volatility

In the viewpoint of Knightian uncertainty, this paper deals with option pricing with jump volatility. First, we prove that the jump volatility model is a Knightian uncertainty problem; then we identify the factors which reflect the Knighitan uncertainty based on k-Ignorance. We find that the option price under Knightian uncertainty is not unique but an interval. Through theoretical analysis and simulation, we conclude that the intensity of Poisson, the jump size, and the maturity date determine the price interval.