Uncertainty Quantification of Derivative Instruments

Abstract

Model and parameter uncertainties are ubiquitous whenever a parametric model is selected to value a derivative instrument. Combining the Monte Carlo method and the Smolyak interpolation algorithm, this paper proposes an accurate and efficient numerical method to quantify the uncertainty embedded in complex derivatives. Except for the value function being smooth with respect to the model parameters, there are no additional requirements on the payoff function or the candidate models. Numerical tests are carried out to quantify the uncertainty of Bermudan put options and down-and-out put options under the Heston model with each model parameter specified in a small interval.

Keywords: Parameter uncertainty; Derivative pricing; Worst-case approach; Smolyak; Monte Carlo; Entropy

JEL Classification: C63; G13; G17