Distributional uncertainty of the financial time series measured by G-expectation

TL;DR

This paper introduces a novel approach using G-normal distribution under nonlinear expectation to measure financial risks, employing autoregressive models and max-mean estimators to predict value at risk with high accuracy.

Contribution

It presents a new method combining G-normal distribution with autoregressive models for risk measurement, outperforming existing VaR predictors.

Findings

G-VaR model predicts VaR effectively on benchmark data.

Autoregressive models determine G-normal distribution parameters.

G-normal distribution captures distributional uncertainty in financial time series.

Abstract

Based on law of large numbers and central limit theorem under nonlinear expectation, we introduce a new method of using G-normal distribution to measure financial risks. Applying max-mean estimators and small windows method, we establish autoregressive models to determine the parameters of G-normal distribution, i.e., the return, maximal and minimal volatilities of the time series. Utilizing the value at risk (VaR) predictor model under G-normal distribution, we show that the G-VaR model gives an excellent performance in predicting the VaR for a benchmark dataset comparing to many well-known VaR predictors.