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

## TL;DR

This paper develops a method to incorporate statistical model error into acceptability pricing of contingent claims by using distributionally robust optimization within a confidence set of models, linking data quality to pricing robustness.

## Contribution

It introduces a novel approach to account for model uncertainty in acceptability prices using a nonparametric neighborhood and dual problem formulation.

## Key findings

- Distributionally robust acceptability prices are derived.
- A large deviations result for nested distance is proved.
- Pricing robustness relates to data quality.

## Abstract

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 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 multi-stage stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we prove a general large deviations result for the nested distance, which allows to relate the bid and ask prices under model ambiguity to the quality of the observed data.