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arXiv · 2203.16292

Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules

Lorenzo Bastianello·Alain Chateauneuf·Bernard Cornet
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Abstract

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

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Lorenzo Bastianello, Alain Chateauneuf, Bernard Cornet. 2022-03-30. Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules. https://arxiv.org/abs/2203.16292

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