Put–Call Parities, absence of arbitrage opportunities, and nonlinear pricing rules

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 Sipos) 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 Sipos pricing rules to be arbitrage free. Finally, we identify violations of the Call-Put Parity with the presence of bid-ask spreads.