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5356Kelly After Trading Frictions 1A trade risks 1 unit. If it wins, it earns gross 1.2 but pays a fee of 0.05. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.56. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5357Kelly After Trading Frictions 2A trade risks 1 unit. If it wins, it earns gross 2 but pays a fee of 0.03. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.48. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5366Effective Spread From Trade Price 1The NBBO is 99.98 bid / 100.02 ask, and a buyer-initiated trade prints at 100.015. What is the effective spread in price terms and in basis points of the prevailing midpoint?金融与交易简单数值题未尝试面试订阅5367Effective Spread From Trade Price 2The NBBO is 49.95 bid / 50.05 ask, and a seller-initiated trade prints at 49.97. What is the effective spread in price terms and in basis points of the prevailing midpoint?金融与交易简单数值题未尝试面试订阅5371Realized Spread And Information Cost 1A buy trade occurs at 100.02 when the midpoint is 100. Five seconds later the midpoint is 100.03. What are the effective spread, realized spread, and adverse-selection component?金融与交易中等数值题未尝试面试订阅5372Realized Spread And Information Cost 2A sell trade occurs at 49.96 when the midpoint is 50. Five seconds later the midpoint is 49.94. What are the effective spread, realized spread, and adverse-selection component?金融与交易中等数值题未尝试面试订阅5376Quoted Effective Realized 1Quotes are 100 bid / 100.06 ask. A signed trade executes at 100.04 and the later midpoint is 100.05. Compute the quoted spread, effective spread, and realized spread.金融与交易中等数值题未尝试面试订阅5377Quoted Effective Realized 2Quotes are 49.92 bid / 50.08 ask. A signed trade executes at 49.95 and the later midpoint is 49.94. Compute the quoted spread, effective spread, and realized spread.金融与交易中等数值题未尝试面试订阅5381Spread Component Mix 1A dealer models the half-spread as order-processing cost 0.008, inventory cost 0.004, and information cost 0.003. What quoted full spread does this imply, and what percentage of the half-spread comes from information risk?金融与交易中等数值题未尝试面试订阅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