# Forecasting Value at Risk with Historical and Filtered Historical Simulation Methods

Value at Risk (VaR) as a branch of risk management has been at the centre of attention of financial managers during past few years, especially after the financial crises in 90’s. And now, after the market failure in 2008, the demand for a precise risk measurement is even higher than before. Risk managers try to review the previous methods, as they think one of the most important causes of the recent crisis was mismanagement of risk.In addition to VaR’s fundamental application which is measuring the risk,it also has other usages related to risk, such as controlling and managing it. VaR as a widespread method is applicable in any kind of institutions which are somehow involved with financial risk, like financial institutions, regulators, nonfinancial corporations or asset managers.There are different approaches to VaR models for estimating the probable losses of a portfolio, which differ in calculating the density function of those losses.The primary VaR methods were based on parametric approaches and some imposed assumptions, which in real cases did not work. One of the most important assumptions could be mentioned as the normal distribution of the density function of the daily returns. Empirical evidence shows the predicted loss or profit by this distribution underestimates the ones in real world.

Contents

1 Introduction
2 Value at Risk
2.1 ‘Risk’ Definition from the Financial Point of View
2.2 VaR
2.3 VaR Formul
3 Historical Simulation and Filtered Historical Simulation Concepts
3.1 HS and FHS
3.1.1 HS
3.1.2 HS Shortcomings
3.1.3 BRW
3.1.4 FHS
3.2 The Most Suitable Time Series Model for our Method: ARMA-GARCH
3.2.1 Volatility
3.2.2 Heteroskedasticity
3.2.3 ARCH, GARCH and ARMA-GARCH Time Series Models
3.3 ARMA-GARCH Preference in Modelling Market Volatility
4 Methodologies of Historical Simulation and Filtered Historical Simulation
4.1 HS
4.2 FHS
4.2.1 Theoretical Method of Obtaining Future Returns
4.2.2 Future Returns Estimation
4.2.3 Simulation of the Future Returns
4.3 Computation of VaR (Same Method in HS and FHS)
5 Empirical Studies
5.1 Daily Returns Plots
5.2 Empirical Study of HS and VaR Computation by HS Method
5.2.1 Empirical Distributions, Forecasting Prices and 1%VaR for 5-Day Horizon
5.2.2 Actual Prices
5.2.3 Comparison
5.3 Empirical Study of FHS and VaR Computation by FHS
Method
5.3.1 Empirical Distributions, Forecasting Prices and 1%VaR for 5-Day Horizon
5.3.2 Comparison
5.4 Running Another Empirical Stud
5.4.1 HS
5.4.2 FH
6 Conclusion
Appendix A (Matlab Source Codes
References

Author: Piroozfar, Ghashang

Source: Uppsala University Library