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4913Liquidity Blind Spot 23Why can a perfectly coherent risk measure still miss a major liquidity problem on a stressed desk?数理金融困难essay未尝试面试订阅4914VaR Aggregation Critique 24Why can a VaR number look reasonable for one desk in isolation yet still be awkward as a firmwide capital aggregator?数理金融困难essay未尝试面试订阅4915Spectral Weight Design 25Why should a spectral risk measure place weakly larger weights on worse outcomes than on mild ones?数理金融困难essay未尝试面试订阅4921Infer Missing Tail Observation 6Sorted empirical losses are [1, 2, 3, 4, 7, 9, 12, x]. Using alpha=0.75, define empirical VaR as the ceil(alpha*n)-th order statistic and empirical ES as the average of losses at and beyond that cutoff. If empirical ES is 11.5, what is x?数理金融中等数值题未尝试面试订阅4922Infer Missing Tail Observation 7Sorted empirical losses are [0, 1, 1, 3, 5, 6, 8, x]. Using alpha=0.875 with the same empirical VaR and ES conventions, if empirical ES is 9.5, what is x?数理金融中等数值题未尝试面试订阅4923Infer Missing Tail Observation 8Sorted empirical losses are [2, 2, 4, 5, 7, 10, 13, x]. Using alpha=0.75 and the same conventions, if empirical ES is 15, what is x?数理金融中等数值题未尝试面试订阅4924Infer Missing Tail Observation 9Sorted empirical losses are [1, 1, 2, 4, 4, 7, 9, x]. Using alpha=0.875 and the same conventions, if empirical ES is 11.5, what is x?数理金融中等数值题未尝试面试订阅4936Tail Severity Interpretation 21Two desks report the same 97.5% VaR, but one desk has a much larger 97.5% ES. What does that tell you about the shape of its tail losses beyond the VaR cutoff?数理金融困难essay未尝试面试订阅4937Backtesting Intuition 22Why is ES harder to backtest directly than VaR in day-to-day risk control?数理金融困难essay未尝试面试订阅4938Scaling Failure Intuition 23Why can square-root-of-time VaR scaling fail badly during volatility clustering?数理金融困难essay未尝试面试订阅4939Tail Preference Intuition 24Why is ES typically preferred to VaR when the main concern is tail severity rather than breach frequency?数理金融困难essay未尝试面试订阅4940Allocation Intuition 25Why is a single firm-wide VaR or ES number not enough for desk incentives unless it is broken into component contributions?数理金融困难essay未尝试面试订阅5011Static Replication Intuition 21Why does the classic static-replication formula for a variance swap involve a strip of OTM options and a log-contract identity?金融与交易困难essay未尝试面试订阅5012Jump-Risk Intuition 22Why can discrete jumps make the simple diffusion-based variance-swap replication less exact?金融与交易困难essay未尝试面试订阅5013Sampling FrequencyWhy can changing the sampling frequency alter a variance swap even if the overall price path looks similar by eye?金融与交易困难essay未尝试面试订阅5014Corridor MotivationWhy might a desk prefer a corridor variance swap to a plain variance swap?金融与交易困难essay未尝试面试订阅5015Mark To Market DriverWhen a variance swap is already running, why does mark-to-market depend on both realized-to-date variance and the market's remaining forward variance?金融与交易困难essay未尝试面试订阅5036EM Mixture Diagnostic 21Why does one EM component sometimes collapse onto a single point with near-zero variance during mixture training?机器学习困难essay未尝试面试订阅5037EM Mixture Diagnostic 22Why can two EM runs on the same data land on noticeably different mixture parameters even when they reach similar likelihoods?机器学习困难essay未尝试面试订阅5038EM Mixture Diagnostic 23Why is label switching not a bug in a mixture model but still a headache when you compare runs?机器学习困难essay未尝试面试订阅