Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals

TL;DR

This paper introduces discrete, non-probabilistic market models that establish arbitrage-free price intervals for European options, connecting trajectory-based properties with classical risk-neutral pricing.

Contribution

It develops a novel framework for discrete, non-probabilistic market models with arbitrage considerations, generalizing martingale properties for option pricing.

Findings

Derived price intervals for European options.

Established connection with risk-neutral pricing.

Allowed limited arbitrage in the market model.

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.