| Summary: | 碩士 === 中原大學 === 財務金融研究所 === 107 === Abstract
The validity of backtesting in value at risk (VaR) has not yet been established even today, mainly because of a lack of effective measurement and the uncertainty of model selections. This study measures the risks involved in the process using the Bootstrap method and Monte Carlo Simulation, and chooses different model assumptions and severity distribution using scoring functions. Then cross-references were made to ascertain whether the estimations are close enough or not. Assumptive models, such as AR-GJRGARCH, AR-EGARCH, and AR-GARCH were used respectively in the process. Expected shortfall (ES) and median shortfall (MS) were both used to captures tail risk, and MS is expected to be a more effective method under the premise of elicitability.
Research results indicate that with Monte Carlo Simulations (applied to three different models so as to obtain estimates), and then scoring functions to choose the right assumption, MS has shown higher stability than ES. This was aligned with our previous expectation. The results generated from bootstrapping indicate that the stability of scoring functions is positively correlated with the size of sample, regardless of model assumptions. Therefore, the present paper concludes that the Bootstrap method exhibits higher stability in risk measurement when sample size is large enough, whilst MS will be a more effective method than ES under the premise of elicitability.
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