有交易成本且支付红利的两值期权定价模型

Binary option pricing model with transaction costs and the payment of dividend

利用对冲的思想和偏微分方法,研究了在交易过程中的两值期权的定价问题.以Black-Scholes模型的基本假设条件为基础,在无风险利率、期望收益率、波动率、红利率均为时间t的函数,以及交易过程中有交易成本和支付红利的假设下,利用无套利原理和偏微分方程的有关理论和方法推导出两值期权中"现金或无值看涨期权(CONC)"的定价公式,并利用CONC的价值与"资产或无值看涨期权(AONC)"的价值关系推导出了AONC的价值.

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 rateμ（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.