美式賣權的提前履約曲線之凸性探討-使用Kim方法

Abstract

我們使用 Kim （1990）論文中的方程式產生出美式賣權之提前履約曲線的數值結果。另外，我們利用此方程式推導出提前履約曲線對時間與殖利率導數的公式。透過對提前履約曲線對殖利率導數的數值結果，我們提出了為何當殖利率高於無風險利率時，提前履約曲線會出現非凸性的原因。我們也解釋了當殖利率高於無風險利率很多時 (大約高於1.5倍)，提前履約曲線會恢復凸性。

We use the equation in Kim (1990) to generate the numerical results of early exercise boundary for the American put options. Then, we evaluate the formula of the derivative of the early exercise boundary with respect to time and dividend yield. By the numerical results of the derivative of the boundary with respect to the dividend yield, we propose reasoning to explain the nonconvexity of the early exercise boundary when the dividend yield is higher than the risk-free rate. And we also explain why the early exercise boundary regains convex when the dividend yield is much higher than the risk-free rate (for approximately q/r > 1.5)