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5800Ladder Width Across Two LevelsA maker posts a two-level ladder on one side. Level 1 at half-spread 0.02 fills with probability 0.5 per round; level 2 at half-spread 0.05 fills with probability 0.2 per round (independent). Each fill carries adverse-selection loss 0.01. Expected PnL per round = sum over levels of fill prob * (h level - 0.01). What is the total expected per-round PnL of the ladder?金融与交易中等数值题未尝试面试订阅5801Width Under A Regime-Switch ForecastBefore a scheduled announcement, the maker believes that during its quote's lifetime the market stays in a calm regime with probability 0.6 (requiring half-spread 0.02) or switches to a stressed regime with probability 0.4 (requiring half-spread 0.10). It sets a single posted half-spread equal to the probability-weighted required width across the two regimes. What half-spread does it quote?金融与交易中等数值题未尝试面试订阅5802Queue Position Versus A Tighter QuoteA maker holds front-of-queue at half-spread 0.06, giving fill probability 0.5 with adverse loss 0.02 per fill. Alternatively it can step one tick tighter to half-spread 0.05, jumping ahead of the whole queue for fill probability 0.8, same 0.02 loss. The metric is fill prob * (h - loss) per round. Which choice has higher expected PnL, and by how much?金融与交易中等数值题未尝试面试订阅5803Minimum Width For A Profit TargetA maker wants to earn at least 5.0 in total net edge over a session in which it expects exactly 250 fills. Each fill earns (h - loss) with adverse-selection loss 0.008, and the maker assumes the fill count is independent of the half-spread over the relevant range. What is the minimum half-spread that meets the target?金融与交易中等数值题未尝试面试订阅5804Width Under Maker-Taker Fee AsymmetryA maker earns a 0.004 rebate when its passive quote is hit. To flatten, 30% of the time it must immediately cross with a marketable order (paying a 0.006 taker fee); the other 70% of the time it flattens passively for another 0.004 rebate. Ignoring adverse-selection moves, what minimum half-spread keeps expected per-fill PnL non-negative, where per-fill PnL = h + entry rebate + expected exit fee?金融与交易困难数值题未尝试面试订阅