Abstract
This paper is concerned with the estimation, forecasting and evaluation of Value-at-Risk (VaR) of Karachi Stock Exchange before and after the global financial crisis of 2008 using Bayesian method. The generalized autoregressive conditional heteroscedastic (GARCH) models under the assumption of normal and heavy-tailed errors are used to forecast one-day-ahead risk estimates. Various measures and backtesting methods are employed to evaluate VaR forecasts. The observed number of VaR violations using Bayesian method is found close to the expected number of violations. The losses are also found smaller than the competing Maximum Likelihood method. The results showed that the Bayesian method produce accurate and reliable VaR forecasts and can be preferred over other methods.
Highlights
Value-at-Risk (VaR) has become a popular tool and is widely used for risk management and capital allocation by financial institutions
Bayesian methods can provide a reasonably good estimates for generalized autoregressive conditional heteroscedastic (GARCH) models. Both these methods are fitted to the daily data of Karachi Stock Exchange returns before and after the global financial crisis
Various evaluation measures and backtesting methods are applied to assess the accuracy of VaR forecast for both estimation methods
Summary
Value-at-Risk (VaR) has become a popular tool and is widely used for risk management and capital allocation by financial institutions. Both underestimation and overestimation of risk could have a negative effect in financial markets. Accurate estimates of VaR is crucial for the financial stability of markets. VaR can be defined as the quantile of the loss, during a specific time period, that can occur within a given portfolio. A precise quantile estimate far out in the left tail of the return distribution is desirable. A thorough survey of risk measures is provided by Jorion (2007)
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