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

Author

Listed:
  • Lorenzo Bastianello

    (Universite Paris 2 Pantheon-Assas, LEMMA, Paris, France)

  • Alain Chateauneuf

    (IPAG Business School, Paris, France and Paris School of Economics and Universite Paris 1, Paris, France)

  • Bernard Cornet

    (Department of Economics, University of Kansas, Lawrence, KS 66045, USA)

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.

Suggested Citation

  • Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2025. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202509, University of Kansas, Department of Economics.
    • Handle: RePEc:kan:wpaper:202509
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    File URL: https://kuwpaper.ku.edu/2025Papers/202509.pdf
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    More about this item

    Keywords

    Asset Pricing; Choquest and/or Sipos pricing; No Arbitrage; Put-Call Parity; Call-Put Parity; Discount Certificate-Call Parity; Market Frictions;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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