带现金成分的美式秃鹰合约：变分不等式方法

中文摘要 AI 辅助

我们研究一种联合执行的美式秃鹰合约，其收益为看涨秃鹰收益加上正现金金额。其平台和正尾部产生两个内部行权边界和两个外部现金行权边界。我们构造了相关变分不等式的唯一有界解，该解在平台两侧均强，并将其与最优停时值等同。我们证明了四个边界的单调性和连续性，并确定了它们在到期时的极限。遵循Broadie和Detemple的方法，我们将内部边界表示为具有相同现金成分的未封顶合约边界的截断。我们还证明了在充分条件下的看涨侧凸性和波动率单调性，显式求解了平稳问题，并给出了数值结果。

英文摘要

We study a jointly exercised American condor contract whose payoff is a call condor payoff plus a positive cash amount. Its plateau and positive tails produce two inner exercise boundaries and two outer cash-exercise boundaries. We construct the unique bounded solution of the associated variational inequality, strong on each side of the plateau, and identify it with the optimal stopping value. We prove monotonicity and continuity of the four boundaries and determine their limits at expiry. Following Broadie and Detemple, we express the inner boundaries as cutoffs of the boundaries of uncapped contracts with the same cash components. We also prove call-side convexity and volatility monotonicity under a sufficient condition, solve the stationary problems explicitly and present numerical results.

发表机构

• Michigan State University（密歇根州立大学）
• Kyungpook National University（庆北国立大学）

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