Revista de la
Unión Matemática Argentina
Trajectorial market models: arbitrage and pricing intervals
Sebastián E. Ferrando, Alfredo L. González, Iván L. Degano, and Massoomeh Rahsepar
Volume 60, no. 1 (2019), pp. 149–185

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The paper develops general, non-probabilistic market models based on trajectory sets and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of a martingale process as well as a generalization that allows a limited notion of arbitrage in the market while still providing coherent option prices. An illustrative example is described in detail. 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.