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5664Why Monte Carlo Beats Trees In High DimensionWhy can Monte Carlo become more attractive than lattice methods as the number of risk factors grows?数理金融中等essay未尝试面试订阅5665Why Monte Carlo And Model Risk InteractWhy does a small Monte Carlo standard error not guarantee that the option price is actually reliable?数理金融中等essay未尝试面试订阅5754Growth Retained at Half-KellyFor a repeatable even-money bet winning with probability 0.60, full Kelly stakes 0.20 of capital. If instead you bet half-Kelly (0.10 of capital), what fraction of the full-Kelly expected log-growth rate do you retain? Give the ratio as a decimal.金融与交易中等数值题未尝试免费5756Growth Rate at a Chosen Overbet FractionA repeatable even-money bet wins with probability 0.60 (full-Kelly fraction is 0.20). A trader instead stakes a fixed 0.30 of capital every round. What is his expected log-growth rate per round, and is it above or below the full-Kelly rate? Give the growth rate as a decimal.金融与交易中等数值题未尝试免费5757Kelly Capped by a Max-Loss LimitA binary bet pays net odds 2-to-1 and you estimate a win probability of 0.60, giving a full-Kelly fraction of 0.40. House policy forbids risking more than 25% of capital on a single position. Since a loss costs the full stake, what fraction should you actually bet, and how is it determined?金融与交易中等数值题未尝试免费5759Kelly Sizing When the Win Probability Is UncertainFor an even-money bet you are unsure of the true win probability: it is equally likely to be 0.52 or 0.62. A colleague plugs the average estimate 0.57 into the Kelly formula and bets 0.14 of capital. To maximize expected log growth you should instead average the realized growth over the two possible true probabilities. Set up the correct objective and state, with a brief reason, whether the growth-optimal stake is at, above, or below 0.14.金融与交易困难数值题未尝试面试订阅5780Avellaneda-Stoikov Reservation ShiftUsing the Avellaneda-Stoikov reservation price r = mid - q*gamma*sigma 2, the mid is 80.00, you are long q = 25 lots, risk aversion gamma = 0.10, and per-step volatility sigma = 0.40 (so sigma 2 = 0.16). How far below the mid is your reservation price, and what is r?金融与交易简单数值题未尝试免费5781Expected Cost Of Holding An Adverse PositionA desk values the risk cost of carrying inventory over one holding period as (gamma/2)*sigma 2*q 2, where gamma = 0.04 is risk aversion, sigma = 2.0 is the per-period price volatility, and q is the position in lots. You are stuck long q = 30 lots. What is the expected risk cost of holding this position for one period?金融与交易简单数值题未尝试免费5782Mark-To-Market On A Stuck LongYou bought 400 shares at an average price of 49.95, capturing 0.05 per share of edge versus the then-fair value of 50.00. The mid has since fallen to 49.70 and you still hold the full 400 shares. On a mark-to-market basis, what is your current total PnL on the position?金融与交易简单数值题未尝试免费5783Cross Now Or Carry The VarianceYou are long q = 20 lots. If you hold, the expected risk cost for the period is (gamma/2)*sigma 2*q 2 with gamma = 0.05 and sigma = 3.0; the expected price drift is zero. If instead you cross the spread and flatten immediately, you pay a certain cost of 0.6 per lot. Compare the two expected costs and decide whether to cross now or carry the position.金融与交易中等数值题未尝试免费5785Asymmetric Quotes From A Long PositionA maker centers quotes on its reservation price r = 100.0 (already shifted below the 100.4 fair mid by a long inventory). It quotes a total spread of 0.20 but, to attract sells, places the ask only 0.06 above r and the bid the remaining width below r. What are the bid and ask prices, and which side sits closer to the fair mid of 100.4?金融与交易中等数值题未尝试免费5786Expected PnL Of Skewing To OffloadYou are long 100 lots. Skewing the ask down attracts an expected sell of 60 lots this period, each lot offloaded at +0.08 of edge versus your reservation price. The 40 lots that remain carry an expected holding cost of 0.15 per lot. What is the expected PnL of the skew policy this period?金融与交易中等数值题未尝试免费5788When To Cross Against A SignalYou are long 500 shares and receive a signal that the mid will fall by an expected 0.04 per share before you could otherwise unwind. Crossing the spread to flatten now costs 0.015 per share for certain. Compare the expected loss from holding through the drift against the certain crossing cost, on the full 500 shares, and decide whether to cross.金融与交易中等数值题未尝试免费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