连续支付喊价式分期付款期权的定价

Valuation of Continuous-installment Shout Option

为了研究连续支付喊价式分期付款期权的定价问题,文章推导了期权价格满足的抛物型变分不等式,并证明了其障碍函数在部分定解区域上存在显式表达式。该变分不等式有2条自由边界:一条是最佳喊价边界,另一条是最佳弃权边界。文章首先通过自由边界的定性分析讨论了这2条自由边界的位置和性质,然后利用惩罚方法求解变分不等式,最后给出不同参数下的数值例子。结果表明:如果无风险利率大于股息收益率,那么当时间远离到期日,最佳喊价边界趋向无穷大;随着到期日的逼近,2条自由边界均趋向于敲定价格;喊价权利和分期付款率均对自由边界有着显著的影响。

In order to study the pricing problem of continuous-installment options,a parabolic variational inequality that the option price satisfies is derived,and the existence of an explicit expression for its barrier function in a subset of the solution domain is proved.The variational inequality has two free boundaries,one is the optimal shouting boundary,and the other is the optimal stopping boundary.The location and properties of these two free boundaries are discussed through qualitative analysis,and the penalty method is used to solve the variational inequalities so as to give numerical examples with different parameters.The results show that if the risk-free interest rate is greater than the dividend yield,the optimal shouting boundary tends to infinity when the time is far from the maturity date;but as the maturity date approaches,both free boundaries tend to strike prices.In addition,both the shouting right and the installment rate have a significant impact on the free boundaries.