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5797Width Sensitivity To Informed FractionOf the flow that fills the maker, a fraction f is informed and costs 0.06 in adverse move; the rest (1-f) is uninformed and costs 0. The maker quotes the break-even half-spread h(f) = f*0.06. By how much must it widen if the informed fraction rises from f=0.20 to f=0.35?金融与交易中等数值题未尝试面试订阅5798Width Snapped To A Tick GridA model says the economically required half-spread is 0.037, but quotes must sit on a tick grid with tick size 0.01 and the maker may only quote half-spreads that are integer multiples of one tick. To avoid quoting below the required edge, the maker rounds up to the nearest admissible half-spread. What half-spread does it quote, and what is the resulting overcharge (excess above the required 0.037)?金融与交易简单数值题未尝试面试订阅5799Width For A Latency-Limited QuoteA maker cannot cancel instantly: from a price signal to its cancel landing there is a fixed exposure window of 50 milliseconds during which its quote is stale. Per-second volatility is 0.4 price units (so variance scales linearly with time). The maker sets its half-spread equal to one standard deviation of the price move over the exposure window. What half-spread does it quote?金融与交易中等数值题未尝试面试订阅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5805EV Per Fill With Rebate And Hedge FeeYou passively fill 300 shares capturing a half-spread of 0.022 per share and earning a maker rebate of 0.0012 per share. To flatten you immediately cross the spread on the hedge leg, paying a taker fee of 0.003 per share. What is the expected PnL for this fill?金融与交易简单数值题未尝试免费5806Breakeven Fill ProbabilityPosting a quote costs you 0.30 in expected order-management and infrastructure cost per quote regardless of outcome. If filled, the quote yields a net profit of 1.50. At what fill probability does the quote break even in expectation?金融与交易简单数值题未尝试免费5807Edge In Ticks To DollarsA futures market maker captures an edge of 0.75 ticks per contract on a fill. Each tick is worth 12.50 dollars per contract and the fill is for 8 contracts. What is the dollar edge on this fill?金融与交易简单数值题未尝试免费5808Net Edge After Adverse SelectionYou capture a half-spread of 0.04 per share when filled. A fraction 0.35 of your fills come from informed traders, and on those fills the fair value moves 0.10 per share against you (uninformed fills have zero subsequent move). What is your expected net edge per fill, per share?金融与交易中等数值题未尝试免费5809EV Comparison Of Two Quote PricesQuote A sits one tick inside: fill probability 0.40, net edge 0.015 per share. Quote B sits one tick wider: fill probability 0.25, net edge 0.028 per share. Both quote 100 shares. Which quote has higher expected PnL, and what is that higher value?金融与交易中等数值题未尝试免费5810Expected Profit Over N QuotesOver a session you post 5000 quotes. Each quote has a fill probability of 0.08, and each fill earns a net edge of 0.25. What is your expected total PnL for the session?金融与交易简单数值题未尝试免费5811Edge Required To Cover Inventory RiskEach fill of 200 shares leaves you holding inventory that carries an expected risk charge of 0.50 until you can hedge. The fill earns rebate of 0.001 per share. What minimum gross half-spread per share must you capture so the fill at least breaks even after the rebate and the inventory charge?金融与交易中等数值题未尝试免费5812Probability-Weighted PnL Of A Skewed QuoteLong inventory, you skew quotes to sell. The ask fills with probability 0.45 earning net edge 0.020 per share; the bid fills with probability 0.10 but is toxic, earning net edge -0.030 per share. Each side quotes 100 shares. Assuming at most one side fills, what is the expected PnL of this skewed quote?金融与交易困难数值题未尝试面试订阅5813Blended EV Across Maker And Taker FillsOf your 1000 fills, 70 percent are passive maker fills earning 0.05 net edge plus a 0.001 rebate per share, and 30 percent are aggressive taker fills earning 0.05 net edge minus a 0.003 fee per share. Every fill is 100 shares. What is your expected total PnL across all fills?金融与交易困难数值题未尝试面试订阅5814Maker Rebate Versus Taker Fee TradeoffPosting passively, you earn a rebate of 0.002 per share but capture only 0.006 of edge with fill probability 0.30. Crossing aggressively, you pay a taker fee of 0.003 per share, capture 0.011 of edge, and fill with certainty. For a 100-share order, which approach has higher expected PnL?金融与交易中等数值题未尝试免费5815EV Across A Fill-Size DistributionWhen your bid is hit, the executed size follows a distribution: 50 shares with probability 0.5, 200 shares with probability 0.3, and 400 shares with probability 0.2. You earn a net edge of 0.02 per share regardless of size. Given that you are filled, what is the expected PnL of the fill?金融与交易中等数值题未尝试免费5816EV With Queue Position And Partial FillYour 300-share quote reaches the front of the queue with probability 0.6. If it does, it fully fills (300 shares); otherwise the queue clears only partway and you fill just 100 shares. Net edge is 0.015 per share in both cases. What is the expected PnL of the quote, accounting for queue position?金融与交易中等数值题未尝试免费