The paper studies market models based on trajectory spaces, properties of such models are obtained without recourse to probabilistic assumptions . For a given European option, an interval of rational pricesexists under a more general condition than the usual no-arbitrage requirement. The paper develops computational results in order to evaluate the option bounds; the global minmax optimization, defining the price interval, is reduced to a local minmax optimization via dynamic programming. A general class of trajectory sets is described for which the market model introduced by Britten Jones and Neuberger is nested as a particular case. We also develop a market model based on an operational setting constraining market movements and investor's portfolio rebalances. Numerical examples are presented, the effect of the presence of arbitrage on the price bounds is illustrated.
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.
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market models based on trajectory spaces, properties of such models are obtained without recourse to probabilistic assumptions
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
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European option, an interval of rational pricesexists under a more general condition
option, there exists an interval bounding the set of possible fair prices; such interval exists under more general conditions
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computational results in order
a backward recursive method
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A general class of trajectory sets is described for which the market model introduced by Britten Jones and Neuberger is
Trajectory sets are introduced for which existing non-probabilistic markets models are
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We also develop a market model based on an operational setting constraining market movements and investor's portfolio rebalances. Numerical
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