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5762Macaulay Duration Of A 3-Year BondA 3-year annual-coupon bond has face 100, coupon rate 7%, and yield to maturity 6%. What is its Macaulay duration in years?金融与交易中等数值题未尝试免费5765Current Yield Of A Discount BondA bond with face 100 pays a 4% annual coupon and currently trades at 92. What is its current yield (in percent)? Is it above or below the bond's yield to maturity?金融与交易简单数值题未尝试免费5769Approximate Yield To MaturityA 4-year annual-coupon bond has face 100, coupon 5, and trades at 95. Using the approximate-YTM formula [C + (F − P)/n] / [(F + P)/2], estimate its yield to maturity (in percent).金融与交易中等数值题未尝试免费5770PV From A Quoted Discount FactorThe market 4-year discount factor is quoted directly as 0.8638. A single cashflow of 250 is due in exactly 4 years. What is its present value?金融与交易简单数值题未尝试面试订阅5771Eight-Year Annuity PVAn ordinary annuity pays 12 at the end of each year for 8 years. The flat discount rate is 0.06. What is its present value?金融与交易中等数值题未尝试面试订阅5772Level Perpetuity PVA perpetuity pays 7 at the end of every year forever, with the first payment one year from now. The discount rate is 0.035. What is its present value?金融与交易简单数值题未尝试面试订阅5773Zero-Coupon Price From YieldA zero-coupon bond pays 100 at maturity in 7 years. Its annually compounded yield is 0.04. What is its price today?金融与交易简单数值题未尝试面试订阅5774Continuous-To-Annual EquivalenceA rate of 0.05 is quoted as continuously compounded. What annually 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5775Effective Annual Rate From Monthly NominalA nominal annual rate of 0.08 is compounded monthly. What is the effective annual rate?金融与交易中等数值题未尝试面试订阅5776PV Under A Non-Flat Discount CurveA bond pays 50 in 1 year, 50 in 2 years, and 1050 in 3 years. The quoted discount factors are 0.97, 0.93, and 0.88 for years 1, 2, and 3. What is its present value?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