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4528Capped Downside Insurance StripA protection strip pays nothing above 85, then increases dollar-for-dollar as S T falls from 85 to 70, but below 70 the protection is capped at 15. What static replication matches it?数理金融中等essay未尝试面试订阅4529Stock Plus Loss Cap 14What static portfolio replicates the payoff S T - (95-S T) + + (80-S T) +?数理金融中等essay未尝试面试订阅4536First Building Blocks for a Flat-Then-Ramp-Then-Flat PayoffA payoff is flat below K1, rises with constant slope 0.4 between K1 and K2, and is flat again above K2. Before writing numbers, what static building blocks should you try first, and why?数理金融中等essay未尝试面试订阅4537Warning Sign for a True Jump in the PayoffA target payoff has a genuine jump discontinuity at strike K, but the desk only has plain vanilla calls and puts at that maturity. What is the first replication warning sign you should notice?数理金融中等essay未尝试面试订阅4539Missing Strike and Exact Static ReplicationA payoff has its key kink at K = 97, but the listed option grid only trades strikes 95 and 100 at the right maturity. What should you conclude first about exact static replication from listed vanillas alone?数理金融中等essay未尝试面试订阅4540Why the Payoff Sketch Comes Before Instrument AlgebraWhen a structured payoff is described verbally, why should you sketch its piecewise graph before choosing any static instrument weights?数理金融中等essay未尝试面试订阅4541Call Superhedge Upper Bound 1European calls with strikes 90 and 110 trade at prices 14 and 5. Using only static positions in these two calls, what is the tightest model-free upper bound you can infer for the price of the call with strike 100?数理金融中等数值题未尝试面试订阅4546Call Subhedge Lower Bound 6European calls with strikes 90 and 110 trade at prices 14 and 5. What is the strongest model-free lower bound you can infer for the price of the call with strike 100 using monotonicity and static sub-hedging?数理金融中等数值题未尝试面试订阅4551Call Price Interval 11Calls with strikes 90 and 120 trade at 18 and 6. What no-arbitrage interval can you infer for the missing call price C(105) using static sub- and super-replication only?数理金融中等数值题未尝试面试订阅4616Replication Inversion 1In a one-step replication setup, S u = 120, S d = 90, the option pays C d = 4 in the down state, and the hedge ratio is Delta = 0.6. What up-state payoff C u is implied?数理金融简单数值题未尝试面试订阅4617Replication Inversion 2In a one-step replication setup, S u = 92, S d = 70, the option pays C u = 16 in the up state, and the hedge ratio is Delta = 13/22. What down-state payoff C d is implied?数理金融简单数值题未尝试面试订阅4618Replication Inversion 3A replicating portfolio holds Delta = 0.5 shares and B = -20 in the bond. If S 0 = 50, what option price does replication imply today?数理金融简单数值题未尝试面试订阅4619Replication Inversion 4If a one-step replicating portfolio has current option price 19.5728, S 0 = 120, and Delta = 0.6, what bond holding B is implied?数理金融简单数值题未尝试面试订阅4620Replication Inversion 5A replicating hedge uses Delta = 0.5333 and bond holding B = -39.6 with no discounting over the step. If S u = 108 and S d = 78, what payoffs does this hedge produce in the up and down states?数理金融简单数值题未尝试面试订阅4641Break-Even Realized Vol From Hedging P&L 1A delta-hedged long option has gamma 0.04, spot 100, implied volatility 0.2, and hedge horizon 0.083 years. Over that horizon, the diffusion-style hedging P&L attributable to volatility mismatch is observed to be 0.6374 using the approximation 0.5*Gamma*S 2*(sigma real 2 - sigma imp 2)*dt. What realized volatility sigma real is implied?数理金融中等数值题未尝试面试订阅4642Break-Even Realized Vol From Hedging P&L 2A delta-hedged long option has gamma 0.03, spot 80, implied volatility 0.25, and hedge horizon 0.167 years. Over that horizon, the diffusion-style hedging P&L attributable to volatility mismatch is observed to be -0.4826 using the approximation 0.5*Gamma*S 2*(sigma real 2 - sigma imp 2)*dt. What realized volatility sigma real is implied?数理金融中等数值题未尝试面试订阅4646Transaction Cost Breakeven 6A hedged option book expects to earn 60 of frictionless gamma/theta edge over the month. It will rebalance 40 times, with average absolute share turnover 120 shares per rebalance. What is the maximum per-share transaction cost that still leaves nonnegative expected net hedging P&L?数理金融简单数值题未尝试面试订阅4648Transaction Cost Breakeven 8A hedged option book expects to earn 37.5 of frictionless gamma/theta edge over the month. It will rebalance 25 times, with average absolute share turnover 200 shares per rebalance. What is the maximum per-share transaction cost that still leaves nonnegative expected net hedging P&L?数理金融简单数值题未尝试面试订阅4666Inverse Spot From Affine Local Vol 1A local-vol surface is parameterized by sigma loc(S,t) = 0.2 + 0.12*(S/100 - 1). At what spot level S does the local volatility equal 0.212?数理金融简单数值题未尝试面试订阅4667Inverse Spot From Affine Local Vol 2A local-vol surface is parameterized by sigma loc(S,t) = 0.18 + -0.08*(S/80 - 1). At what spot level S does the local volatility equal 0.188?数理金融简单数值题未尝试面试订阅