Enhancing Extreme Risk Assessment in Green Bonds: A Monte Carlo Simulation Approach

Abstract

This research aims to develop a Monte Carlo framework that uses a semi-parametric approach to model tail events, moving beyond the assumptions of normal distribution. The methodology involves customizing the Monte Carlo simulation to incorporate non-Gaussian distributions, such as the student t-distribution, which accounts for heavier tails and time-varying volatility. Additionally, the study explores the application of particle filtering algorithms to further refine the Monte Carlo simulation process. The research contrasts traditional Geometric Brownian Motion (GBM) models with modified versions that better capture extreme events. Empirical analysis is conducted using data from FactSet, focusing on daily log returns of GBs and Global Clean Energy (GCE) indexes. The study tests the effectiveness of Monte Carlo simulations in estimating Value at Risk (VaR) and Expected Shortfall (ES) under extreme conditions. The findings suggest that using t-distributions and volatility models like GARCH leads to more robust estimations of VaR and ES compared to conventional methods. By shifting from a normal to a t-distribution, I aimed to fit a more realistic distribution of returns. This adjustment decreased the exceedance level to match the 95% confidence level, reducing it from 28 in two years with a normal distribution to 19 with a t-distribution in GBs. Additionally, I incorporated the volatility term, another impactful factor in GBM, by fitting a GARCH model to sample data. This further decreased the exceedance level from 28 in two years to 12. However, incorporating both modifications led to a robust estimation of VaR with 95% CL. On the other hand, particle filtering did not significantly affect the results.