Stylized Model of Lévy Process in Risk Estimation

Abstract

Risk management is a popular and important problem in academia and industry. From a small-scale system, such as city logistics, to a large-scale system, such as the supply chain of a global industrial or financial system, efficient risk management is required to prevent loss from uncertainty. In this paper, we assume that risk factors follow the Lévy process, and propose a stylized model, based on regression, that can estimate the risk of a complicated system under the framework of nest simulation. Specifically, portfolio risk estimation using the Lévy process is discussed as an example. The stylized model simplifies the risk factors artificially, and provides useful basis functions to fit the portfolio loss with little computational effort. Numerical experiments showed the good performance of the stylized model in estimating risk for the Variance Gamma process and the Normal Inverse Gaussian process, which are two examples of the Lévy process.