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5777Breakeven Rate Of Two CashflowsYou pay 80 today and receive 100 in exactly 2 years. What annually compounded discount rate sets the present value of the deal to zero (its breakeven rate)?金融与交易中等数值题未尝试面试订阅5778Semiannual-Compounding PVA cashflow of 100 is due in 3 years. The rate is 0.06, quoted as a nominal annual rate compounded semiannually. What is the present value?金融与交易中等数值题未尝试面试订阅5779Annual-To-Continuous EquivalenceAn annually compounded rate of 0.06 is given. What continuously compounded rate produces the same one-year discount factor?金融与交易中等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5784Where The Inventory Limit BindsA maker keeps adding to a long position only while the per-lot edge it still captures, 0.30, exceeds the marginal inventory risk it takes on, modeled as gamma*sigma 2*q with gamma = 0.02 and sigma 2 = 0.25. Beyond what position size q does the marginal inventory risk exceed the edge, defining the maker's effective long-side inventory limit?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5787How Far To Skew Given InventoryHolding inventory q = 40, your base reservation shift below mid is lambda*q with lambda = 0.01, i.e. 0.40. You believe an adverse downward drift of 0.60 will hit before you can offload, and you want your effective quote center to drop by at least the full 0.60 to keep encouraging sells. By what additional multiplicative factor (1 + s) must you scale the base 0.40 skew, and what is s?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