Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals

Abstract

The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a generalization that allows a limited notion of arbitrage in the market while still providing coherent option prices. Several properties of the price bounds are obtained, in particular a connection with risk neutral pricing is established for trajectory markets associated to a continuous-time martingale model.

Version 2, from June 12, 2015, supersedes the version of July 7 2014. The changes are numerous and substantial. Version3, November 4, 2015, much polished version, notation and notions consistent with sequel paper (appearing as reference [12] in this version)