On Bounds for Model Calibration Uncertainty

Abstract

For a given derivative pricing model and an exotic product, one can ask the following natural question: if the model prices calibration instruments within their bid/ask spreads (or generally, given the model calibration error), what is the uncertainty of the exotic product valuation? This model calibration uncertainty can be defined through the coherent model risk measure of R.Cont. Here we give lower and upper bounds for this measure, which only depend on the stochastic dynamics specified by the model and its calibration, but not on a particular choice of the modelling parameters, and discuss a series of related questions.