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5441Choose Width 1A market maker can quote half-spread 0.01 with fill prob 0.48, half-spread 0.02 with fill prob 0.32, or half-spread 0.04 with fill prob 0.18. Expected adverse-selection loss per fill is 0.008 and rebate is 0.001. Which width maximizes expected round EV?金融与交易中等数值题未尝试面试订阅5446Volatility Buffer Width 1A desk uses half-spread = base + k*sigma 1s*sqrt(horizon seconds) + buffer. With base=0.004, sigma 1s=0.08, horizon=4, k=1.1, and buffer=0.002, what half-spread should it quote?金融与交易简单数值题未尝试面试订阅5450Volatility Buffer Width 5A desk uses half-spread = base + k*sigma 1s*sqrt(horizon seconds) + buffer. With base=0.0045, sigma 1s=0.07, horizon=25, k=1, and buffer=0.001, what half-spread should it quote?金融与交易简单数值题未尝试面试订阅5451Required Widening 1A market maker wants net edge 0.018 per fill after adverse-selection loss. If expected loss is 0.007, rebate is 0.001, and current half-spread is 0.012, what half-spread is required and how much extra widening is needed?金融与交易中等数值题未尝试面试订阅5456Tight Versus Wide 1Choice A is half-spread 0.018 with per-side fill prob 0.34. Choice B is half-spread 0.028 with per-side fill prob 0.24. Expected loss per fill is 0.009, rebate is 0.001, and fixed inventory penalty is 0.0015 per round. Which quote has higher expected value?金融与交易中等数值题未尝试面试订阅5461Why One Tick Is Not Always OptimalWhy is quoting the minimum possible spread not automatically optimal for a market maker?金融与交易中等essay未尝试面试订阅5462Why Width Should Follow SpeedWhy should the same instrument often be quoted wider in a fast tape than in a slow tape?金融与交易中等essay未尝试面试订阅5463Why Competition Only Helps If Fills Improve EnoughWhy does matching a tighter competitor only make sense if the fill-rate gain is large enough?金融与交易中等essay未尝试面试订阅5464Why Good Width Cannot Fix Bad MidWhy can a mathematically reasonable width still lose money if the quote center is wrong?金融与交易中等essay未尝试面试订阅5465Why Width And Skew Are Different ControlsWhy do market makers treat quote width and quote skew as different levers?金融与交易中等essay未尝试面试订阅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