Abstract
Most of the financial institutions compute the Value-at-Risk (VaR) of their trading portfolios using historical simulation-based methods. In this paper, we examine the Filtered Historical Simulation (FHS) model introduced by Barone-Adesi et al. (1999) theoretically and empirically. The main goal of this study is to find an answer for the following question: “Does the assumption on innovation process play an important role for the Filtered Historical Simulation model?”. For this goal, we investigate the performance of FHS model with skewed and fat-tailed innovations distributions such as normal, skew normal, Student’s-t, skew-T, generalized error, and skewed generalized error distributions. The performances of FHS models are evaluated by means of unconditional and conditional likelihood ratio tests and loss functions. Based on the empirical results, we conclude that the FHS models with generalized error and skew-T distributions produce more accurate VaR forecasts.
Highlights
The most well known risk measure, Value-at-Risk (VaR), is used to measure and quantify the level of financial risk within a firm or investment portfolio over a specific holding period
The approaches to VaR could be investigated in three categories: (i) fully parametric models approach based on a volatility models; (ii) non-parametric approaches based on the Historical Simulation (HS) methods and (iii) Extreme Value Theory approach based on modeling the tails of the return distribution
We investigate Filtered Historical Simulation (FHS) models with skewed and fat-tailed innovation distributions both theoretically and empirically
Summary
The most well known risk measure, Value-at-Risk (VaR), is used to measure and quantify the level of financial risk within a firm or investment portfolio over a specific holding period. The VaR measures the potential loss of risky asset or portfolio over a defined period and for a given confidence level. The approaches to VaR could be investigated in three categories: (i) fully parametric models approach based on a volatility models; (ii) non-parametric approaches based on the Historical Simulation (HS) methods and (iii) Extreme Value Theory approach based on modeling the tails of the return distribution. The HS model is based on the assumption that historical distribution of returns will remain the same over the periods. The one-day-ahead VaR R forecast for HS model is given by
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