Trajectory based models. Evaluation of minmax pricing bounds

Ivan Degano, Sebastian Ferrando and Alfredo Gonzalez

Papers from arXiv.org

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.

Date: 2015-11, Revised 2016-12
New Economics Papers: this item is included in nep-cmp
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Published in Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2018, Vol 25, 97-128

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1511.01207

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