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5397No-Loss Quote After Order Flow 2Value is either 49 or 51 with prior P(high)=0.45. If value is high, the probability of a sell order is 0.22; if value is low, it is 0.75. You observe a sell order and must set the break-even bid. What price avoids expected loss?金融与交易中等数值题未尝试面试订阅5400No-Loss Quote After Order Flow 5Value is either 149 or 151.5 with prior P(high)=0.35. If value is high, the probability of a buy order is 0.77; if value is low, it is 0.24. You observe a buy order and must set the break-even ask. What price avoids expected loss?金融与交易中等数值题未尝试面试订阅5401Break-Even Spread Under Informed Flow 1Suppose the true value is equally likely to be 99.8 or 100.2. A fraction 0.3 of traders are informed and always trade in the correct direction; the rest are noise traders who buy or sell with equal probability. A dealer posts symmetric quotes around the prior mean. What break-even half-spread, bid, and ask should the dealer use?金融与交易中等数值题未尝试面试订阅5406Spread Under Event Risk 1A dealer currently uses a half-spread of 0.05. Ahead of an event, the informed-trader fraction is estimated at 0.12 and the value jump size at 0.4. In the symmetric informed-flow model, what is the dealer's expected value per trade if the old spread is left unchanged, and how much extra half-spread is needed to get back to break-even?金融与交易中等数值题未尝试面试订阅5411Why Getting Hit Is Bad NewsWhy does a passive market maker often interpret being lifted or hit as bad news about value?金融与交易中等essay未尝试面试订阅5412Why Spreads Widen Before EventsWhy do dealers often widen materially ahead of earnings or macro releases even if the pre-event midpoint looks calm?金融与交易中等essay未尝试面试订阅5413Why Noise Flow Helps MakersWhy does a higher fraction of uninformed noise flow usually make passive quoting more profitable?金融与交易中等essay未尝试面试订阅5414Why Price Improvement Can Be ToxicWhy can an aggressive dealer who price-improves by a tiny amount still lose money if the flow is informed?金融与交易中等essay未尝试面试订阅5415Why Lower Signal Quality Narrows Posterior MovesIf buy and sell flow become less informative, why should the dealer's posterior fair value move less after each trade?金融与交易中等essay未尝试面试订阅5416Posterior Fair Value From Noisy Signal 1Your prior fair value estimate is 100 with variance 1. A fresh signal arrives at 100.6 with variance 0.25. If you fuse them by precision weighting, what posterior fair value should you quote around?金融与交易中等数值题未尝试面试订阅5417Posterior Fair Value From Noisy Signal 2Your prior fair value estimate is 50 with variance 0.64. A fresh signal arrives at 49.7 with variance 0.16. If you fuse them by precision weighting, what posterior fair value should you quote around?金融与交易中等数值题未尝试面试订阅5418Posterior Fair Value From Noisy Signal 3Your prior fair value estimate is 75.5 with variance 0.81. A fresh signal arrives at 76.1 with variance 0.36. If you fuse them by precision weighting, what posterior fair value should you quote around?金融与交易中等数值题未尝试面试订阅5421Cross-Instrument Fair Value Update 1Current mid is 50. Your model says fair value should move by 0.6 times the futures move and 0.4 times the peer basket move. If futures move 0.8 and the peer basket move is 0.3, what updated fair value do you get?金融与交易简单数值题未尝试面试订阅5422Cross-Instrument Fair Value Update 2Current mid is 100. Your model says fair value should move by 0.45 times the futures move and 0.7 times the peer basket move. If futures move -1.1 and the peer basket move is -0.2, what updated fair value do you get?金融与交易简单数值题未尝试面试订阅5423Cross-Instrument Fair Value Update 3Current mid is 75.5. Your model says fair value should move by 0.8 times the futures move and 0.3 times the peer basket move. If futures move 0.35 and the peer basket move is 0.25, what updated fair value do you get?金融与交易简单数值题未尝试面试订阅5424Cross-Instrument Fair Value Update 4Current mid is 20. Your model says fair value should move by 1.1 times the futures move and 0.6 times the peer basket move. If futures move -0.12 and the peer basket move is 0.05, what updated fair value do you get?金融与交易简单数值题未尝试面试订阅5426Expected Fair Value Across Scenarios 1Your fast book model gives three possible fair values: 99.6 with p=0.2, 100 with p=0.5, 100.9 with p=0.3. If you quote around the expected fair value, what number should you use?金融与交易简单数值题未尝试面试订阅5427Expected Fair Value Across Scenarios 2Your fast book model gives three possible fair values: 49.2 with p=0.25, 50.1 with p=0.45, 50.7 with p=0.3. If you quote around the expected fair value, what number should you use?金融与交易简单数值题未尝试面试订阅5431Stale Print Adjustment 1Current mid is 100. A stale print was 100.4 when the mid at that time was 99.9. You only trust 0.5 of that old deviation now, and a fresh peer signal adds 0.06. What fair value do you get?金融与交易中等数值题未尝试面试订阅5432Stale Print Adjustment 2Current mid is 50.2. A stale print was 49.8 when the mid at that time was 50. You only trust 0.3 of that old deviation now, and a fresh peer signal adds -0.04. What fair value do you get?金融与交易中等数值题未尝试面试订阅