A Comparison between Historical Simulation and GARCH Model for Estimating Value-at-Risk: Case of Indian Stock Exchange

Financial risk management has always been an important issue across all the countries economy, however, it gained greater attention in the surprising aftermath of the subprime mortgage crisis in the USA. Questions were raised regarding the quantitative techniques used by banks and other financial institutions for measuring their financial risk. Generally, Value-at-risk is one of the main statistical techniques used by banks for modeling financial risk allowed by the regulators. Therefore the present study intends to examine the performance of parametric and non-parametric models of Value-at-Risk (VaR) under different variables to determine the suitability and superiority of a model in a given economic situation. Further, the study considered two most common measure of VaR i.e. Historical Simulation (non-parametric model) and GARCH model (parametric model). We aim to analyze the performance of both the models over three estimation periods (250 days, 500 days and 500 days) and to examine how the performance of the models varies with a change in estimation period. We feel this study is one of its kind that tests the adequacy of VaR models for different rolling windows and different confidence levels for Nifty 50 returns for the data period of around 26 years. The study establishes the superiority of Historical Simulation over the GARCH model for computing VaR. The empirical testing suggests that the non-parametric model can obtain successful VaR measures over the parametric model, given the advantage of freedom from theoretical assumption that no specific form for the return distribution needs to be hypothesized.