第 1 / 2 页
非代码面试题
显示 20 / 23 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
5391Posterior Value After A Buy 1The asset value is either 99 or 101. Prior P(high)=0.45. If the value is high, a buyer arrives with probability 0.8; if the value is low, a buyer arrives with probability 0.25. You observe a buy order. What is the posterior probability that the value is high, and what is the posterior fair value?金融与交易中等数值题未尝试面试订阅5393Posterior Value After A Buy 3The asset value is either 74 or 76.5. Prior P(high)=0.4. If the value is high, a buyer arrives with probability 0.85; if the value is low, a buyer arrives with probability 0.35. You observe a buy order. What is the posterior probability that the value is high, and what is the posterior fair value?金融与交易中等数值题未尝试面试订阅5394Posterior Value After A Buy 4The asset value is either 19.5 or 20.5. Prior P(high)=0.55. If the value is high, a buyer arrives with probability 0.7; if the value is low, a buyer arrives with probability 0.2. You observe a buy order. What is the posterior probability that the value is high, and what is the posterior fair value?金融与交易中等数值题未尝试面试订阅5396No-Loss Quote After Order Flow 1Value is either 99 or 101 with prior P(high)=0.5. If value is high, the probability of a buy order is 0.82; if value is low, it is 0.28. 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5827A dealer faces order flow where a fraction 0.4 of traders arA dealer faces order flow where a fraction 0.4 of traders are informed (always trade in the correct direction) and 0.6 are noise traders who buy or sell with equal probability. The true value is equally likely high or low, so informed traders buy half the time and sell half the time. You observe a buy order. What is the probability that the trader who just bought is informed?金融与交易中等数值题未尝试面试订阅5828True value is either 50 (low) or 60 (high), equally likely. True value is either 50 (low) or 60 (high), equally likely. A fraction 0.25 of order flow is informed and trades in the correct direction; the remaining 0.75 is noise that buys or sells 50/50. A dealer is hit on the bid (a sell order arrives) and gets filled. What is the dealer's expected loss per share relative to true value, i.e. the expected adverse move E[bid - V | sell], if the bid is quoted at the prior mean 55?金融与交易困难数值题未尝试面试订阅5829In a market the per-trade adverse-selection cost to a dealerIn a market the per-trade adverse-selection cost to a dealer is alpha*delta, where alpha is the informed fraction and delta is the value gap. Noise traders are willing to pay at most a half-spread of 0.30 before they stop trading entirely. The value gap is delta = 1.0. Above what informed fraction alpha does the market break down (no spread can both cover adverse selection and retain noise traders)?金融与交易困难数值题未尝试面试订阅5830A dealer has just observed a buy order and updated the posteA dealer has just observed a buy order and updated the posterior probability that value is high to 0.70 (value high = 102, low = 98). A second buy order then arrives. In this model informed traders buy when value is high with probability 0.9 and when value is low with probability 0.1 (noise component already folded in). Treating the post-first-trade posterior as the new prior, what is the posterior P(high) after the second buy, and the new fair value?金融与交易中等数值题未尝试面试订阅5831Over a short window a dealer observes 7 buys and 3 sells. EaOver a short window a dealer observes 7 buys and 3 sells. Each trade is independently a buy with probability p, where p = 0.5 in the no-news state and p = 0.7 in the good-news state. The two states are equally likely a priori. Using the order imbalance as the signal, what is the posterior probability that the market is in the good-news state?金融与交易困难数值题未尝试面试订阅5832A dealer's clientele is 20% informed and 80% noise on the cuA dealer's clientele is 20% informed and 80% noise on the current trade. Informed traders, when present, always pick the profitable side; noise traders are random. The dealer has just been adversely picked off (filled on the wrong side). Going into the NEXT incoming order, the dealer believes nothing about the population has changed. What is the unconditional probability that the next order comes from an informed trader, and why is this the right number to price against rather than 0%?金融与交易中等数值题未尝试面试订阅5833A dealer quotes a two-sided market and earns the half-spreadA dealer quotes a two-sided market and earns the half-spread s on every fill. A fraction alpha = 0.15 of fills are informed and cost the dealer the full value gap delta = 0.8 (the dealer is on the wrong side for the entire move). The remaining fills are noise and the dealer keeps s. The dealer wants expected profit per trade of at least 0.02. What is the minimum half-spread s the dealer must charge?金融与交易中等数值题未尝试面试订阅