标题： 无套利与流动性美式期权对冲 显示英文标题

标题： No-arbitrage and hedging with liquid American options

摘要： 由于大多数交易的个股期权是美式期权，因此有必要将半静态交易中获得的结果推广到允许静态交易美式期权的情况。 然而，由于持有与做空此类期权的头寸具有不对称性，这个问题至今仍难以解决。 在这里，我们提供了一个统一的框架，并将arXiv:1502.06681（即将发表于《应用概率年鉴》）中的资产定价基本定理（FTAP）和对偶性推广到投资者也可以做空美式期权的情况。 遵循arXiv:1502.06681，我们假设持有的美式期权是可分的。 而对于做空的美式期权，我们证明了可分性在套利性质和对冲价格方面不起作用。 然后使用arXiv:1604.05517中提出的扩展概率空间的方法，我们将做空的美式期权转换为欧式期权，并在扩展空间中建立了FTAP以及在有无模型不确定性情况下的次对冲和超对冲对偶性。 显示英文摘要

摘要： Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positions of holding versus shorting such options. Here we provide a unified framework and generalize the fundamental theorem of asset pricing (FTAP) and hedging dualities in arXiv:1502.06681 (to appear in Annals of Applied Probability) to the case where the investor can also short American options. Following arXiv:1502.06681, we assume that the longed American options are divisible. As for the shorted American options, we show that the divisibility plays no role regarding arbitrage property and hedging prices. Then using the method of enlarging probability spaces proposed in arXiv:1604.05517, we convert the shorted American options to European options, and establish the FTAP and sub- and super-hedging dualities in the enlarged space both with and without model uncertainty.