永久美式交叉期权(英文)

Perpetual American straddle option

本文主要利用变分不等式的比较原理,研究永久美式交叉期权的最佳实施边界.研究发现,这是一个自由边界问题.与标准永久美式期权不同,这种期权在股票分红时有两个自由边界点,而当股票不分红时仅有一个自由边界点.这些自由边界点确定了相应的美式交叉期权最佳实施边界的范围,与其金融背景相符.

By appplying the comparison principle for the variational inequality, we ana- lyzed the behavior of exercise boundaries for the perpetual American straddle option. We found that it is a free boundary problem. Different from the standard perpetual American option, it has two exercise boundary points with dividends and only one free boundary point without dividends. These results can be understood very well from the financial point of view. We will present a rigorous mathematical proof, and find the bounds of exercise boundaries for the American straddle option with finite expiry.