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5516Reservation Price 1A market maker uses reservation price = fair value - lambda*inventory. If fair value is 100, inventory is 50, lambda is 0.006, and the chosen half-spread is 0.02, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5517Reservation Price 2A market maker uses reservation price = fair value - lambda*inventory. If fair value is 50, inventory is -80, lambda is 0.004, and the chosen half-spread is 0.015, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5518Reservation Price 3A market maker uses reservation price = fair value - lambda*inventory. If fair value is 75.5, inventory is 120, lambda is 0.003, and the chosen half-spread is 0.018, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5519Reservation Price 4A market maker uses reservation price = fair value - lambda*inventory. If fair value is 20.1, inventory is -40, lambda is 0.008, and the chosen half-spread is 0.012, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5521Passive Unwind Versus Crossing 1You are long 300 shares. If you skew passively and wait, you fully unwind with probability 0.4 and earn 0.012 per share; if the unwind does not happen, you expect a mark-to-market loss of 0.008 per share on the remaining position. Alternatively, you can cross the spread now and pay 0.005 per share. Which action has higher expected PnL?金融与交易中等数值题未尝试面试订阅5526Required Skew 1Without skew, expected bid-fill probability is 0.32 and ask-fill probability is 0.18. If you increase ask-side skew by s, bid-fill probability becomes 0.32 - 0.02*s and ask-fill probability becomes 0.18 + 0.015*s. What is the smallest nonnegative s that makes expected inventory change no longer positive?金融与交易中等数值题未尝试面试订阅5531Expected Ending Inventory 1You start long 200 shares. If you keep both sides on, expected bid-fill probability is 0.24, ask-fill probability is 0.16, and each fill size is 50. If you instead turn the bid off and only leave the ask quote live, what expected ending inventory do you get under each policy, and which policy leaves you closer to flat?金融与交易中等数值题未尝试面试订阅5536Why Long Inventory Changes The MidWhy does holding a large long inventory typically shift a market maker's practical quote center below the estimated fair value?金融与交易中等essay未尝试面试订阅5537Why Immediate Unwind Can Be RationalWhy might a market maker rationally cross the spread to reduce inventory even though crossing is mechanically costly?金融与交易中等essay未尝试面试订阅5538Why One-Sided Quoting ExistsWhy do market makers sometimes stop quoting one side entirely instead of merely widening both sides?金融与交易中等essay未尝试面试订阅5539Why Inventory And Information Risk InteractWhy is a bad inventory state especially dangerous when adverse selection is also high?金融与交易中等essay未尝试面试订阅5540Why Inventory Policy Needs More Than Spread MathWhy is inventory management usually not solvable by one static spread formula alone?金融与交易中等essay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