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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5441Choose Width 1A market maker can quote half-spread 0.01 with fill prob 0.48, half-spread 0.02 with fill prob 0.32, or half-spread 0.04 with fill prob 0.18. Expected adverse-selection loss per fill is 0.008 and rebate is 0.001. Which width maximizes expected round EV?金融与交易中等数值题未尝试面试订阅5446Volatility Buffer Width 1A desk uses half-spread = base + k*sigma 1s*sqrt(horizon seconds) + buffer. With base=0.004, sigma 1s=0.08, horizon=4, k=1.1, and buffer=0.002, what half-spread should it quote?金融与交易简单数值题未尝试面试订阅5450Volatility Buffer Width 5A desk uses half-spread = base + k*sigma 1s*sqrt(horizon seconds) + buffer. With base=0.0045, sigma 1s=0.07, horizon=25, k=1, and buffer=0.001, what half-spread should it quote?金融与交易简单数值题未尝试面试订阅5451Required Widening 1A market maker wants net edge 0.018 per fill after adverse-selection loss. If expected loss is 0.007, rebate is 0.001, and current half-spread is 0.012, what half-spread is required and how much extra widening is needed?金融与交易中等数值题未尝试面试订阅5466One-Sided Quote EV 1A one-sided quote has fill probability 0.28. If filled, size is 200, half-spread capture is 0.018 per share, rebate is 0.001, and expected adverse-selection loss is 0.01 per share. What is the expected PnL?金融与交易简单数值题未尝试面试订阅5471Two-Sided Quote EV 1You quote both sides for size 150. Bid-fill probability is 0.22 and ask-fill probability is 0.3. Bid half-spread is 0.016, ask half-spread is 0.02, rebate is 0.001, bid-side adverse loss is 0.009, and ask-side adverse loss is 0.012. What is expected PnL?金融与交易中等数值题未尝试面试订阅5476Partial Fill EV 1A quote can fill in two sizes: with probability 0.25 you trade 100 shares and earn 0.012 raw edge per share; with probability 0.1 you trade 250 shares and earn 0.009 raw edge per share. Rebate is 0.0005 per share in either case. What is expected PnL?金融与交易简单数值题未尝试面试订阅5491Two-Round Opportunity Value 1In round 1, a quote has fill probability 0.3 and edge 0.02 if filled. If it does not fill, you get a round-2 opportunity with fill probability 0.25 and edge 0.028. Assume a round-1 fill ends the game because your risk limit is used up. What is total expected edge?金融与交易中等数值题未尝试面试订阅5516Reservation Price 1A market maker uses reservation price = fair value - lambda*inventory. If fair value is 100, inventory is 50, lambda is 0.006, and the chosen half-spread is 0.02, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5517Reservation Price 2A market maker uses reservation price = fair value - lambda*inventory. If fair value is 50, inventory is -80, lambda is 0.004, and the chosen half-spread is 0.015, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5518Reservation Price 3A market maker uses reservation price = fair value - lambda*inventory. If fair value is 75.5, inventory is 120, lambda is 0.003, and the chosen half-spread is 0.018, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5519Reservation Price 4A market maker uses reservation price = fair value - lambda*inventory. If fair value is 20.1, inventory is -40, lambda is 0.008, and the chosen half-spread is 0.012, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5521Passive Unwind Versus Crossing 1You are long 300 shares. If you skew passively and wait, you fully unwind with probability 0.4 and earn 0.012 per share; if the unwind does not happen, you expect a mark-to-market loss of 0.008 per share on the remaining position. Alternatively, you can cross the spread now and pay 0.005 per share. Which action has higher expected PnL?金融与交易中等数值题未尝试面试订阅5526Required Skew 1Without skew, expected bid-fill probability is 0.32 and ask-fill probability is 0.18. If you increase ask-side skew by s, bid-fill probability becomes 0.32 - 0.02*s and ask-fill probability becomes 0.18 + 0.015*s. What is the smallest nonnegative s that makes expected inventory change no longer positive?金融与交易中等数值题未尝试面试订阅5531Expected Ending Inventory 1You start long 200 shares. If you keep both sides on, expected bid-fill probability is 0.24, ask-fill probability is 0.16, and each fill size is 50. If you instead turn the bid off and only leave the ask quote live, what expected ending inventory do you get under each policy, and which policy leaves you closer to flat?金融与交易中等数值题未尝试面试订阅