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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4693Time Until Only 20% of a Variance Shock RemainsA mean-reverting stochastic-vol model has kappa = 2. After how many years is only 20% of the initial variance shock expected to remain?数理金融简单数值题未尝试面试订阅4694Expected One-Year Forward VarianceIn a mean-reverting stochastic-vol model, current variance is v0 = 0.09, long-run mean is theta = 0.04, and mean-reversion speed is kappa = 1.5. What is E[v 1]?数理金融简单数值题未尝试面试订阅4698Annualized Volatility from Expected Forward VarianceCurrent variance is v0 = 0.04, long-run mean is theta = 0.09, mean-reversion speed is kappa = 2, and horizon is T = 0.5. What expected forward variance E[v T] and annualized volatility sqrt(E[v T]) does the model imply?数理金融中等数值题未尝试面试订阅4701Stochastic Vol Scenario 11Why can stochastic volatility explain a persistent equity-index downside skew more naturally than a constant-volatility Black-Scholes model?数理金融中等essay未尝试面试订阅4702Stochastic Vol Scenario 12What does vol-of-vol control economically in a stochastic-vol model?数理金融中等essay未尝试面试订阅4703Stochastic Vol Scenario 13Why is mean reversion in variance such a central ingredient of practical stochastic-vol models?数理金融中等essay未尝试面试订阅4704Stochastic Vol Scenario 14What dynamic feature can stochastic volatility generate that deterministic local-vol surfaces often struggle to reproduce?数理金融中等essay未尝试面试订阅4706Stochastic Vol Diagnostic 16If mean-reversion speed kappa rises while other parameters stay fixed, what happens to the persistence of a volatility shock?数理金融中等essay未尝试面试订阅