We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.

中文翻译：

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外来期权的一致上限价格

我们考虑为奇异期权寻找一致的价格上限的问题，这些期权的收益取决于两个不同预定时间点的股票价格（例如亚洲期权），给定这些到期日观察到的看涨价格的数量有限。使用无模型方法，仅考虑（贴现）股票价格过程在无套利条件下是鞅。如果收益是定向凸的，我们将获得最坏情况下的边际定价措施。当观察到的股票价格数量增加时，决定了价格上限的收敛速度。我们用一些数值计算来说明我们的发现。