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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5817Expected Edge Under Cancel RiskPer posted quote you normally capture 0.030 of net edge. On 20 percent of posts a price move makes your quote stale before you trade; you cancel successfully on 70 percent of those stale cases (avoiding the trade entirely), but on the remaining stale cases you are picked off and lose 0.080 per share instead of earning the edge. The other 80 percent of posts fill normally at the full edge. What is your expected net edge per posted quote?金融与交易困难数值题未尝试面试订阅5818Quote Both Sides Or One SideQuoting only the ask: fill probability 0.40, net edge 0.025 per share. If you also add a bid, the ask economics are unchanged, but the bid fills with probability 0.30 at a net edge of -0.020 per share (its flow is toxic given your view). Each side is 100 shares. Which is better, quoting one side or both, and what is the higher expected PnL?金融与交易中等数值题未尝试免费5821Expected Fills Over Many RoundsYou post the same two-sided quote in each of 8 independent rounds. In every round the quote fills with probability 0.35, and there is no inventory limit so fills do not interact. What is the expected number of fills over the 8 rounds?金融与交易简单数值题未尝试免费5822Cumulative PnL With Inventory CarryoverOver 3 rounds you quote to buy 1 unit each round when filled. Round 1 fills at price 100, round 2 fills at price 101, round 3 does not fill. After round 3 the unit is marked at fair value 102. Each unit also costs 0.10 in carry per round it is held to the end of round 3. What is total expected PnL, counting markup minus total carry?金融与交易中等数值题未尝试面试订阅5824Learning Your Fill RateYour unknown per-round fill probability is either 0.2 (prior 0.5) or 0.5 (prior 0.5). You quote 3 independent rounds and observe exactly 2 fills. What is the posterior probability that the true fill probability is 0.5?金融与交易中等数值题未尝试面试订阅5825Reprice After An Informative FillYour round-1 bid fills. A fill is more likely when an informed seller is present, so after a fill you assign probability 0.6 to fair value having dropped by 0.05 (and 0.4 to no change). In round 2 you re-quote and earn raw edge 0.04 if filled, with fill probability 0.5, but you also still hold the round-1 unit which loses the fair-value drop. What is the expected round-2 PnL including the revaluation of the held unit?金融与交易困难数值题未尝试面试订阅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5835Two venues route flow to your quotes. Venue A flow is 5% infTwo venues route flow to your quotes. Venue A flow is 5% informed; Venue B flow is 40% informed. Both have the same value gap delta = 0.5, and informed flow costs you delta per fill while you earn half-spread s = 0.10 on all fills. You can only post on one venue. Compute expected profit per fill on each venue, and explain in one line which venue you choose and the adverse-selection reason.金融与交易中等数值题未尝试面试订阅