# Unified Bayesian Conditional Autoregressive Risk Measures using the Skew Exponential Power Distribution

## TL;DR

This paper introduces a unified Bayesian framework for risk measurement using the Skew Exponential Power distribution, incorporating non-linearity with P-splines and demonstrating effectiveness on stock market data.

## Contribution

It proposes a novel unified Bayesian approach for risk measures with a flexible non-linear extension using P-splines, adapting MCMC for inference.

## Key findings

- Effective risk measurement on stock data
- Flexible modeling of non-linearity
- Improved asymmetry handling

## Abstract

Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices.