Securities with Mixture of Elliptic Distributed Risk Factors

Title: Securities with Mixture of Elliptic Distributed Risk Factors

Abstract: This research article explores the estimation of Value-at-Risk (VaR) and Expected Shortfall for a quadratic portfolio of securities, specifically equities, without the use of Delta and Gamma Greeks. The study focuses on elliptic distributed risk factors, using Monte Carlo methods to estimate the VaR and Expected Shortfall. The authors provide a methodology for calculating these values, using special attention to mixture of normal and t-student distributions. The results of the study suggest that the proposed method can be used to estimate the VaR and Expected Shortfall for quadratic portfolios of equities, providing valuable insights for risk management in the financial sector.

Main Research Question: How can we estimate the Value-at-Risk and Expected Shortfall for a quadratic portfolio of securities without the use of Delta and Gamma Greeks, using Monte Carlo methods and elliptic distributed risk factors?

Methodology: The study uses Monte Carlo methods to estimate the VaR and Expected Shortfall for a quadratic portfolio of securities. The authors focus on elliptic distributed risk factors, which are a generalization of normal distributions. They provide a methodology for calculating these values, using special attention to mixture of normal and t-student distributions.

Results: The study presents an explicit equation with a solution for the VaR when the joint log-returns follow a specific mixture of elliptic distributions. The results suggest that the proposed method can be used to estimate the VaR and Expected Shortfall for quadratic portfolios of equities.

Implications: The findings of this study have important implications for the financial sector. By providing a method for estimating the VaR and Expected Shortfall for quadratic portfolios of equities without the use of Delta and Gamma Greeks, the study offers a more accurate and efficient approach to risk management. This can lead to better decision-making processes and improved financial stability.

Link to Article: https://arxiv.org/abs/0310043v2 Authors: arXiv ID: 0310043v2