Using the method of hedging and partial differential, the problem of binary option pricing is discussed. Based on the hypothesis of Black-Scholes model, the CONC pricing equation in the binary option is deduced under the assumption that the risk-free rate r(t), expected return rate μ(t), volatility σ(t), and the dividend q(t) are all function of t and there exist transaction costs and dividends during the process of transaction by arbitrage-free principle and partial differential equation. AONC pricing equation in the binary option is obtained according to the relationship between CONC and AONC.

transaction cost; dividend; binary option