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5789Skew To Recover From A ShortYou start short q0 = -150 shares; lot size is 50. Under a symmetric quote, bid-fill probability is 0.30 and ask-fill probability is 0.30. Under a bid-skew policy designed to buy back, bid-fill probability rises to 0.50 while ask-fill probability falls to 0.20. Compute the expected ending inventory under each policy, and state which leaves you closer to flat.金融与交易中等数值题未尝试免费5790Optimal Width Under Linear Fill DecayPer-side fill probability falls linearly with half-spread: p(h) = 0.6 - 4*h for h in [0, 0.15]. Net edge per fill is (h - loss) with loss = 0.01. Expected single-side PnL per round is p(h)*(h - loss). What half-spread h maximizes it?金融与交易中等数值题未尝试面试订阅5791Width From Volatility DoublingA desk sets half-spread proportional to expected holding-period volatility: h = c*sigma*sqrt(T). It currently quotes h=0.05 at sigma=0.02 per unit-sqrt-time and T=1. If realized volatility doubles to sigma=0.04 and expected holding time rises to T=4, what half-spread should it quote (same c)?金融与交易简单数值题未尝试面试订阅5792Break-Even Width Against Adverse SelectionWhen a resting quote fills, with probability 0.30 it is an informed pick-off that moves 0.05 against the maker; with probability 0.70 it is noise flow with zero adverse move. Ignoring rebates, what minimum half-spread makes expected per-fill PnL exactly zero?金融与交易中等数值题未尝试面试订阅5793Undercut Or Match Under CompetitionA competitor quotes half-spread 0.04. If the maker matches at 0.04 it shares the queue and wins 40% of a 0.04-edge round, with adverse loss 0.012 per fill on fills it wins; fill volume is 100 rounds. If it undercuts to 0.03 it captures 100% of fills but earns only 0.03 edge with the same 0.012 loss. Per-round edge net of loss times fills won is the metric. Which is better and by how much?金融与交易困难数值题未尝试面试订阅5794Inventory Inflates The Sell-Side WidthA maker is long inventory q=200 units. It widens the side that would add to its position using h buy = base + gamma*sigma2*q and tightens nothing else, with base=0.02, gamma=0.0001, sigma2=2 (variance). What half-spread does it quote on the buy side (where filling makes it longer)?金融与交易中等数值题未尝试面试订阅5795Width Versus Expected Fill RateOver a fixed window, expected fills per minute are 10 at half-spread 0.02, 6 at 0.05, and 3 at 0.09. Net edge per fill is (h - 0.01). Total expected PnL per minute = fills * (h - 0.01). Which half-spread maximizes throughput-adjusted PnL?金融与交易中等数值题未尝试面试订阅5796Minimum Width To Clear FeesA venue charges a 0.003 taker-removal fee that the maker effectively pays when it must cross to flatten, and the maker pays a 0.002 clearing fee per fill but receives a 0.0015 maker rebate. Expected adverse-selection loss is 0.004 per fill. What minimum half-spread leaves non-negative expected PnL per fill?金融与交易中等数值题未尝试面试订阅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