Incorporating statistical model error into the calculation of acceptability prices of contingent claims

Optimal bid and ask prices for contingent claims can be found by stochastic optimization. However, the underlying stochastic model for the asset price dynamics is typically based on data and statistical estimation. We define a... [ view full abstract ]

Optimal bid and ask prices for contingent claims can be found by stochastic optimization. However, the underlying stochastic model for the asset price dynamics is typically based on data and statistical estimation. We define a confidence set by a nonparametric neighborhood of an estimated 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. Some examples illustrate our results.