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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5819Edge Per Unit Of RiskA quote earns an expected net edge of 0.018 per fill, and the PnL of each fill has a standard deviation of 0.12. What is the edge-per-unit-of-risk (expected edge divided by standard deviation) for this quote? Give the answer to three decimals.金融与交易简单数值题未尝试免费5820Expected Daily PnL From Volume And Fill RateThe product trades 2,000,000 shares per day. You are at the touch on enough of that flow that you fill 4 percent of daily volume passively, capturing a net edge of 0.0015 per share after all costs. What is your expected daily 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5823Optimal Skew After A FillAfter a round-1 buy fill leaves you long 1 unit, you choose a round-2 quote skew s (in cents) that shifts both quotes down to encourage a sell. Selling probability is 0.3 + 0.1*s and expected edge per sell is 0.05 - 0.01*s, for s between 0 and 5. Round-2 expected edge is (selling probability)*(edge). Which integer s in 0,1,2,3,4,5 maximizes round-2 expected edge?金融与交易困难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5826Expected Wait Until First FillYou repost the same quote every round; each round it fills independently with probability 0.2. Rounds continue indefinitely until the first fill. What is the expected number of rounds until (and including) the first fill?金融与交易简单数值题未尝试免费5837Roll Implied Spread From AutocovarianceUnder Roll's model, transaction price changes have a first-order serial autocovariance of -0.0009 (in price-squared units). Estimate the implied effective spread.金融与交易中等数值题未尝试面试订阅5838Round-Trip Half-Spread CostQuotes are 80.00 bid / 80.10 ask and stay constant. A trader buys 500 shares at the ask, then later sells the same 500 shares at the bid. What is the total dollar cost of crossing the spread on the round trip, and what is it as a multiple of the half-spread per share?金融与交易简单数值题未尝试面试订阅5839Relative Spread In Basis PointsStock A trades around 20.00 with a quoted spread of 0.04; stock B trades around 200.00 with a quoted spread of 0.30. Express each quoted spread in basis points of its midpoint, and state which name is more expensive to cross on a relative basis.金融与交易简单数值题未尝试面试订阅5840Long Strangle Break-EvensA long strangle buys a put with strike 95 for premium 2 and a call with strike 105 for premium 3, where 105>95. What are the lower and upper break-even prices at expiry, and the total distance between them?金融与交易简单数值题未尝试免费5842Long Call Butterfly ProfileA long call butterfly buys one 90 call, sells two 100 calls, and buys one 110 call for a net debit of 2 (strikes equally spaced). What is the maximum profit, the stock price at which it occurs, and the maximum loss?金融与交易中等数值题未尝试免费5843Long Call Break-Even and Loss FloorYou buy a single call with strike 50 for premium 4. What is the break-even stock price at expiry, the maximum possible loss, and the profit if the stock ends at 61?金融与交易简单数值题未尝试免费