English

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

Theoretical Economics 2022-03-31 v1

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

Cite

@article{arxiv.2203.16292,
  title  = {Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules},
  author = {Lorenzo Bastianello and Alain Chateauneuf and Bernard Cornet},
  journal= {arXiv preprint arXiv:2203.16292},
  year   = {2022}
}