连续支付美式分期付款期权的计算

Valuation of American continuous-installment options

为了研究连续支付分期付款美式期权的定价问题,以看涨期权为例,采用对冲的方法建立了此类期权定价的偏微分方程模型.模型中的方程是一个非齐次的Black-Scholes方程,其非齐次项为期权的分期付款率.根据金融意义,连续支付分期付款美式期权的定价问题是一个自由边界问题,含有最佳终止边界和最佳实施边界2条自由边界,从而把偏微分方程模型转化为相应的变分不等方程模型,然后用有限差分方法给出了此类期权价格的数值解,并分析了不同参数值的情况下最佳终止边界和最佳实施边界的位置及性质.结果表明看涨期权的最佳终止边界单调非减,而最佳实施边界则单调非增.

In order to pricing American style continuous installment options, hedging was used to establish a Partial Differential Equation （PDE） model for call options. The PDE inthe model is a nonhomogeneous Black Scholes equation. The nonhomogeneous term is the installment rate. In the financial field, the problem can be expressed as a free boundary problem with two free boundaries： the optimal stop boundary and the optimal exercise boundary. Then the PDE model can be transformed into a variation inequality prob lem. By using the finite-difference method, some numerical results were obtained and displayed. The optimal stop boundary and the optimal exercise boundary were calculated and analyzed with different parameter values. The results show that the optimal stopping boundarg of call option is monotone and not decreasing, while the optimal exercise boundary is monotone and not creasing.