When prices of assets traded in a financial market are determined by nonlinear pricing rules, different parities between call and put options have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity‐sensitive (Choquet and/or Šipoš) pricing rules, that is, pricing rules that can be represented via discounted expectations with respect to non‐additive probability measures. We analyze how nonadditivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Šipoš pricing rules to be arbitrage free. Finally, we identify violations of the Call‐Put Parity with the presence of bid–ask spreads.

中文翻译：

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看跌期权平价、缺乏套利机会和非线性定价规则

当金融市场上交易的资产价格由非线性定价规则确定时，会考虑看涨期权和看跌期权之间的不同平价。我们证明，在单调性下，看涨期权和看跌期权以及折扣证书之间的平价表征了模糊敏感（Choquet 和/或 Šipoš）定价规则，即可以通过相对于非可加概率度量的贴现期望来表示的定价规则。我们分析了非可加性与套利机会的关系，并给出了 Choquet 和 Šipoš 定价规则无套利的充分必要条件。最后，我们通过买卖差价来识别看涨期权平价的违反情况。