论文标题
连续时间圆锥形的极端措施
Extreme Measures in Continuous Time Conic Finace
论文作者
论文摘要
动态频谱风险度量将索赔的估值范围定义为对索赔的最高期望，对索赔的预期对一套主导的措施的回报。达到这种极值的措施称为极端措施。我们确定相对于共同的主导度量的ra-nykodim衍生物的显式表达式。根据发现的公式，我们估计了两种情况下的极端度量。首先，对选项的中价进行校准，估值范围由期权竞标和询问价格给出。其次，从历史股票价格估计的主导措施和估值范围由历史5天高和低价给出。在这两个实验中，我们都发现市场通过测试场景来决定上限，在这些方案中，在主导度量下，损失显着低于预期，而在基本情况下仅略低的损失的下限。
Dynamic spectral risk measures define a claim's valuation bounds as supremum and infimum of expectations of the claim's payoff over a dominated set of measures. The measures at which such extrema are attained are called extreme measures. We determine explicit expressions for their Radon-Nykodim derivatives with respect to the common dominating measure. Based on the formulas found, we estimate the extreme measures in two cases. First, the dominating measure is calibrated to mid prices of options and valuation bounds are given by options bid and ask prices. Second, the dominating measure is estimated from historical mid equity prices and valuation bounds are given by historical 5-day high and low prices. In both experiments, we find that the market determines upper bounds by testing scenarios in which losses are significantly lower than expected under the dominating measure, while lower bounds by ones in which gains are only slightly lower than in the base case.
