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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4671Regime Time Fraction From RMS Local Vol 6Along one realized path, local volatility equals 0.22 for a fraction f of the year and 0.3 for the rest. If the path-consistent RMS local volatility is observed to be 0.2709, what fraction f of the year was spent in the first regime?数理金融中等数值题未尝试面试订阅4676Local Vol Scenario 11Why can a local-vol model fit today's vanilla surface exactly while still generating unrealistic smile dynamics tomorrow?数理金融中等essay未尝试面试订阅4677Local Vol Scenario 12What does a local-vol model try to absorb into the state variable S that a stochastic-vol model would instead place into an extra state variable?数理金融中等essay未尝试面试订阅4678Local Vol Scenario 13Why does path dependence show up naturally when people criticize local-vol dynamics?数理金融中等essay未尝试面试订阅4679Local Vol Scenario 14Why is Dupire intuition often described as 'backing out an instantaneous local variance surface from vanilla prices'?数理金融中等essay未尝试面试订阅4680Local Vol Diagnostic 15Before trusting a local-vol calibration, what should you inspect first besides raw fit error?数理金融中等essay未尝试面试订阅4681Local Vol Diagnostic 16If sigma loc(S,t) slopes upward in S, what happens to local volatility after a spot rally in that model?数理金融中等essay未尝试面试订阅4682Local Vol Diagnostic 17If sigma loc(S,t) slopes downward in S, what happens to local volatility after a spot selloff?数理金融中等essay未尝试面试订阅4683Local Vol Diagnostic 18If the local-vol surface becomes more curved across spot, what usually happens to path sensitivity?数理金融中等essay未尝试面试订阅4684Local Vol Diagnostic 19Why can two local-vol calibrations with similarly low fit error still imply very different future option behavior?数理金融中等essay未尝试面试订阅4685Local Vol Diagnostic 20Why do the dynamic shortcomings of local vol often become more visible on longer maturities?数理金融中等essay未尝试面试订阅4686Local Vol Diagnostic 21Before using a local-vol model for risk, what should you ask first about the intended use case?数理金融中等essay未尝试面试订阅4687Local Vol Diagnostic 22Before overinterpreting a local-vol surface slope, what should you check first about the data that produced it?数理金融中等essay未尝试面试订阅4688Local Vol Diagnostic 23Before comparing a local-vol surface across two calibration dates, what should you align first?数理金融中等essay未尝试面试订阅4689Local Vol Diagnostic 24Before saying local vol 'explains' skew, what distinction should you make first?数理金融中等essay未尝试面试订阅4690Local Vol Diagnostic 25Before blaming local vol for every dynamic mismatch, what baseline should you check first?数理金融中等essay未尝试面试订阅