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Quantification of risk positions under model uncertainty is of crucialimportance from both viewpoints of external regulation and internal management.The concept of model uncertainty, sometimes also referred to as modelambiguity. Although we know the family of models, we cannot precisely decidewhich 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 valuein such a range is referred to as a worst-case value, and the correspondingmodel is called a worst scenario. Value-at-Risk(VaR) has become a very popularrisk-measurement tool since it was first proposed. Naturally, WVaR(worst-caseValue-at-Risk) attracts the attention of many researchers. Although manyliteratures investigated WVaR, the implications for empirical data analysisremain rare. In this paper, we proposed a special model uncertainty marketmodel to simply the $\mathcal{P}$ to a set contain finite number of probabilitydistributions. The model has the structure of the two-layer mixed distributionmodel. We used change point detection method to divide the returns series andthen 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 fourfinancial markets and then analyzed their different performance.

calculation worst-case Value-at-Risk prediction using empirical data under model uncertainty