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Trajectory based models. Evaluation of minmax pricing bounds

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  • Ivan Degano
  • Sebastian Ferrando
  • Alfredo Gonzalez

Abstract

The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to take place at a finite number of occasions but not bounded in number nor necessarily equally spaced in time. For a given option, there exists an interval bounding the set of possible fair prices; such interval exists under more general conditions than the usual no-arbitrage requirement. The paper develops a backward recursive method to evaluate the option bounds; the global minmax optimization, defining the price interval, is reduced to a local minmax optimization via dynamic programming. Trajectory sets are introduced for which existing non-probabilistic markets models are nested as a particular case. Several examples are presented, the effect of the presence of arbitrage on the price bounds is illustrated.

Suggested Citation

  • Ivan Degano & Sebastian Ferrando & Alfredo Gonzalez, 2015. "Trajectory based models. Evaluation of minmax pricing bounds," Papers 1511.01207, arXiv.org, revised Dec 2016.
    • Handle: RePEc:arx:papers:1511.01207
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Mark Britten-Jones & Anthony Neuberger, 1996. "Arbitrage pricing with incomplete markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 347-363.
    3. repec:dau:papers:123456789/10794 is not listed on IDEAS
    4. 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.
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