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Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals

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  • Sebastian E. Ferrando
  • Alfredo L. Gonzalez
  • Ivan L. Degano
  • Massoome Rahsepar

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.

Suggested Citation

  • Sebastian E. Ferrando & Alfredo L. Gonzalez & Ivan L. Degano & Massoome Rahsepar, 2014. "Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals," Papers 1407.1769, arXiv.org, revised Nov 2015.
    • Handle: RePEc:arx:papers:1407.1769
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    References listed on IDEAS

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    1. Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," CREATES Research Papers 2013-38, Department of Economics and Business Economics, Aarhus University.
    2. Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," Papers 1310.7857, arXiv.org, revised Aug 2014.
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    5. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
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    7. Mark Britten-Jones & Anthony Neuberger, 1996. "Arbitrage pricing with incomplete markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 347-363.
    8. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    9. Jacob Abernethy & Rafael M. Frongillo & Andre Wibisono, 2012. "Minimax Option Pricing Meets Black-Scholes in the Limit," Papers 1202.2585, arXiv.org.
    10. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
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    Cited by:

    1. Ivan Degano & Sebastian Ferrando & Alfredo Gonzalez, 2015. "Trajectory based models. Evaluation of minmax pricing bounds," Papers 1511.01207, arXiv.org, revised Dec 2016.

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