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

2022/03/30 by Lorenzo Bastianello, Bastianello, Lorenzo, Alain Chateauneuf +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #FOS: Economics and business #Financial Markets and Investment Strategies #Law, Economics, and Judicial Systems #Theoretical Economics (econ.TH)

paper · pdf · doi:10.48550/arxiv.2203.16292

openalex publication_date 2022/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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