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

Lorenzo Bastianello, Alain Chateauneuf and Bernard Cornet
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Lorenzo Bastianello: Universite Paris 2 Pantheon-Assas, LEMMA, Paris, France
Bernard Cornet: Department of Economics, University of Kansas, Lawrence, KS 66045, USA

No 202509, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

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.

Keywords: Asset Pricing; Choquest and/or Sipos pricing; No Arbitrage; Put-Call Parity; Call-Put Parity; Discount Certificate-Call Parity; Market Frictions (search for similar items in EconPapers)
JEL-codes: C71 D81 G12 (search for similar items in EconPapers)
Date: 2025-04
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