ABSTRACT The Value at Risk (VaR) is a risk measure that is widely used by financial institutions to allocate risk. Optimal conditional VaR estimates are typically generated using a likelihood function based on the check-loss function. However, issues such as VaR's bias estimation and asymmetric financial decision-making, based on the sign of the forecast error, can result in the use of combined losses or of intractable likelihood functions. In such cases, likelihood function intractability gives ground for Bayesian inference using likelihood-free methods such as the Approximate Bayesian Computation (ABC) one. This method generates posterior estimates when the likelihood function is analytically unavailable. Here, we introduce a novel ABC-MCMC algorithm based on asymmetric kernel density functions that allows for the asymmetric decision-making rule used in VaR estimation. We illustrate this method in CAViaR models where VaR is forecast using simulated and real financial data series.

中文翻译：

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具有非对称内核的 CAVIaR 模型的 ABC 方法

摘要 风险价值（VaR）是金融机构广泛用于分配风险的一种风险度量。最佳条件 VaR 估计通常使用基于检查损失函数的似然函数生成。然而，诸如基于预测误差符号的 VaR 偏差估计和非对称财务决策等问题可能导致使用组合损失或难以处理的似然函数。在这种情况下，似然函数的难易性为使用无似然方法（例如近似贝叶斯计算 (ABC)）的贝叶斯推理提供了基础。当似然函数在分析上不可用时，此方法会生成后验估计。这里，我们引入了一种基于非对称核密度函数的新型 ABC-MCMC 算法，该算法允许在 VaR 估计中使用非对称决策规则。我们在 CAVIaR 模型中说明了这种方法，其中使用模拟和真实金融数据系列预测 VaR。