  Quantification of risk positions under model uncertainty is of crucial
importance from both viewpoints of external regulation and internal management.
The concept of model uncertainty, sometimes also referred to as model
ambiguity. Although we know the family of models, we cannot precisely decide
which one to use. Given the set $\mathcal{P}$, the value of the risk measure
$\rho$ varies in a range over the set of all possible models. The largest value
in such a range is referred to as a worst-case value, and the corresponding
model is called a worst scenario. Value-at-Risk(VaR) has become a very popular
risk-measurement tool since it was first proposed. Naturally, WVaR(worst-case
Value-at-Risk) attracts the attention of many researchers. Although many
literatures investigated WVaR, the implications for empirical data analysis
remain rare. In this paper, we proposed a special model uncertainty market
model to simply the $\mathcal{P}$ to a set contain finite number of probability
distributions. The model has the structure of the two-layer mixed distribution
model. We used change point detection method to divide the returns series and
then used EM algorithm to estimate the parameters. Finally, we calculated VaR,
WVaR(worst-case Value-at-Risk) and BVaR(best-case Value-at-Risk) for four
financial markets and then analyzed their different performance.
