Optimal bid and ask prices for contingent claims can be found by mathematical optimization. To do so, a model for the market dynamicsis needed. While the traditional replication or superreplication strategies find the optimal prices under the constraint that all risks are shifted to the counterparty, we weaken this assumption here by introducing risk (resp. acceptability) functionals in the stochastic optimizationframework. Moreover, we consider the associated ambiguity problem, where we replace the single probability model by a non-parametric set of models . We show that weakening the acceptability constraint leads to a shrinking bid-ask spread while considering model ambiguity makes the bid-ask spread even larger. Some algorithms and numerical examples are presented .
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics . Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model for the underlying asset price process is typically based on data and found by a nonparametric statistical estimation procedure. We define a confidence set of possible estimated models by a nonparametric neighborhood of a baseline model. This neighborhood serves as ambiguity set for a stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we relate the bid and ask prices under model ambiguity to the quality of the observed data .
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Optimal bid and ask prices for contingent claims can be found by mathematical optimization. To do so, a
The determination of acceptability prices of contingent claims requires the choice of a stochastic
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market dynamicsis needed. While the traditional replication or superreplication strategies find the optimal prices under the constraint that all risks are shifted to the counterparty, we weaken this assumption here by introducing risk (resp. acceptability) functionals in the stochastic optimizationframework. Moreover, we consider the associated ambiguity problem, where we replace the single probability model by a non-parametric set of models
underlying asset price dynamics
R
We show that weakening the acceptability constraint leads to a shrinking bid-ask spread while considering model ambiguity makes the bid-ask spread even larger. Some algorithms and numerical examples are presented
Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model for the underlying asset price process is typically based on data and found by a nonparametric statistical estimation procedure. We define a confidence set of possible estimated models by a nonparametric neighborhood of a baseline model. This neighborhood serves as ambiguity set for a stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we relate the bid and ask prices under model ambiguity to the quality of the observed data