Abstract: Traditional option pricing theories were based on the strict assumptions about underlying asset price process, which did not take Knightian uncertainty into consideration.In this article, those strict assumptions are relaxed and options are priced with only up to third order moment information.Due to limited information and the uncertainty of underlying price distribution, the option price can not be priced accurately.To derive upper and lower bounds for option prices with limited information, we build a programming model and solve the dual problem of this model.A comparative analysis between price bounds and Black-Scholes price is done afterwards.The bounds interval with up to third order moment information is narrower than those with only first and second order moment information.In the empirical research of Hong Kong's Hang Seng Index warrants, we find that the market prices indeed lie within the bounds.When volatility and remaining duration is small, upper and lower bounds interval is quite narrow.With this method, we can enhance the robustness of option pricing model, and help investors make investment decisions combining option price bounds and their subjective judgments.

Key words: Knightian uncertainty, upper and lower bounds, dual program, risk neutral pricing