Simulate and estimate volatility by GARCH with/without leverage, riskmetriks. VaR compute and test on VaR Violation. These codes use the package rugarch for Volatitly models.

Code files

1. Financial_Econometrics.R: clean, summarize, and plot the daily return data
2. garch_simulation.R: simulate and compare the performance of different GARCH models under different distribution
3. interval_graph.R: compare the estimated intervals of coefficient from different set-up of simulation
4. garch_estimate.R: GARCH and Value-ar-Risk estimate on daily return data + diagnostics in-sample/out-sample

To understand more details about the performance and mechanism of GARCH, we start with the simulation under different set-ups and distribution of error. We use nlminb() for the maximum lilekihood methods in GARCH.

Several models would be applied: GARCH and GARCH-with leverage (eGARCH, TGARCH, APARCH). By AIC and BIC, GARCH(2,1) and eGARCH(2,1) outperforms.

There are six models: (GARCH, eGARCH) x ("ged", "norm", "std"). They would be assessed in both in-sample and out-sample set.

We compute the VaR in-sample and out-sample (given theorerical distibutrion). Then create the hit sequence $H_t$ and conduct 3 tests in the behavior of VaR violations.