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

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  • Lorenzo Bastianello
  • Alain Chateauneuf
  • Bernard Cornet

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, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    • Handle: RePEc:arx:papers:2203.16292
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    References listed on IDEAS

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