リスク管理の測定規準

最近金融業界のリスク管理に使われているVaRに関する論文を読んでいます。
Steps involved in computing Value at Risk are:
1. Mark portfolio to market
2. Create a distribution of portfolio returns
3. Calculate the VaR
Assumptions about financial markets' distributions in these methods are:
1. leptokurtosis- high peaks and "fat tails" compared to Gaussian
2. negatively skewed for equities
3. volatilities tend to cluster, i.e. they are stable in the short run. I am not sure I understand the basis for this assumption
At any rate, VaR is defined to be the maximum amount a financial institution can lose with a probability theta over a given time horizon.
Models discussed in the paper are grouped into "parametric" and "non-parametric" categories. I am not sure what is meant by "parametric", but I assume that the parameter is time. Thus, the max amount which could be lost with a probability of 5% is given for a specific time, and it will differ between times t and t+1.
One parametric model cited is GARCH. The ARCH in this family of models stands for "autoregressive conditional heteroskedasticity". Heteroskedastic systems are sets of variables with differing variances.
The GARCH equations are:
y(t) = sigma(t)epsilon(t)
sigma^2 = omega + a*y(t-1)^2+b*sigma(t-1)^2
y is the return, sigma is the volatility, and epsilon is the residual. I am not sure what epsilon actually is here. Is it some sort of experimental error? It seems that returns are translated to distributions using a distribution of epsilon. Epsilon is assumed to be normally distributed, so it seems that returns in this case will also be normally distributed. I am not sure how omega, a, or b are chosen. The autoregression seems to be he expression of volatility at t in terms of volatility at t-1.