Trajectory based models. Evaluation of minmax pricing bounds
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.
Keywords
Cite
@article{arxiv.1511.01207,
title = {Trajectory based models. Evaluation of minmax pricing bounds},
author = {Ivan Degano and Sebastian Ferrando and Alfredo Gonzalez},
journal= {arXiv preprint arXiv:1511.01207},
year = {2018}
}
Comments
45 pages, 15 figures. This is the second version of the paper. There is a somewhat different example that connects to known probabilistic models. Some results along this direction are presented. We also discuss the literature pertaining to the computation of fair price bounds