To price options using replication in imperfect markets, both Knightian uncertainty and transaction cost have to be taken into account. In this paper, we put an uncertainty factor into volatility, assume investors minimize the root mean square error of replication when they choose hedging ratio, and derive European option price by a recursive procedure. To avoid high transaction cost caused by continuous hedging, we establish a discrete and binomial replication model considering both uncertainty and transaction cost. Numerical examples imply that option price contains both risk premium and uncertainty premium, and it is an approximately linearly increasing function of transaction cost but a nonlinearly increasing function of uncertainty. Additionally, both uncertainty and transaction cost have effects on the price of the at-the-money option, but they almost have no impact on the price of deeply in-the-money or out-of-the-money options. Empirical analysis of the Shanghai 50ETF options market indicates that the Black–Scholes model tended to underestimate the market price, whereas our model better estimates market prices.

为了在不完善的市场中使用复制定价期权，必须同时考虑奈特的不确定性和交易成本。在本文中，我们将不确定性因素纳入波动率中，假设投资者选择对冲比率时将复制的均方根误差最小化，并通过递归程序得出欧洲期权价格。为了避免由于连续对冲而产生的高交易成本，我们建立了兼顾不确定性和交易成本的离散二项式复制模型。数值例子表明，期权价格既包含风险溢价又包含不确定性溢价，并且它是交易成本的近似线性增加的函数，但是却具有不确定性的非线性增加的函数。此外，不确定性和交易成本都会影响平价期权的价格，但它们几乎对价内或价外期权的价格没有影响。对上海50ETF期权市场的经验分析表明，Black-Scholes模型往往低估了市场价格，而我们的模型则更好地估计了市场价格。