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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4691Variance Shock Half-Life 1A mean-reverting stochastic-vol model has mean-reversion speed kappa = 1.5. What is the half-life of a variance shock?数理金融简单数值题未尝试面试订阅4692Remaining Variance-Shock Fraction After Nine MonthsA mean-reverting stochastic-vol model has variance drift d v t = kappa(theta-v t)dt + ... with kappa = 1.2. What fraction of an initial variance shock v 0-theta is expected to remain after 0.75 years?数理金融简单数值题未尝试面试订阅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4695Expected Variance Drop Over Six MonthsIn a mean-reverting stochastic-vol model, variance starts at v0 = 0.16, long-run mean is theta = 0.09, and kappa = 1. What is the expected drop v0 - E[v 0.5 ] after half a year?数理金融简单数值题未尝试面试订阅4696Fair Average Variance Over Horizon 6In a mean-reverting stochastic-vol model, variance starts at v0 = 0.04, long-run mean is theta = 0.09, mean-reversion speed is kappa = 1.5, and horizon is T = 1. What expected average variance E[(1/T)∫ 0 T v s ds] and annualized volatility sqrt of that average variance does the model imply?数理金融中等数值题未尝试面试订阅4697Long-Run Mean Implied by an Average-Variance TargetSuppose expected average variance over one year is E[(1/T)∫ 0 T v s ds] = 0.097927 in a mean-reverting stochastic-vol model with current variance v0 = 0.12, kappa = 1, and T = 1. What long-run mean theta is implied?数理金融中等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4699Starting Variance Implied by an Average-Variance TargetA stochastic-vol model has long-run mean theta = 0.05, mean-reversion speed kappa = 1, and horizon T = 1. If expected average variance over that year is 0.081606, what starting variance v0 is implied?数理金融中等数值题未尝试面试订阅4700Mean-Reversion Speed Implied by a One-Year Forward Variance TargetA stochastic-vol model has current variance v0 = 0.16 and long-run mean theta = 0.04. If the expected variance one year ahead is E[v 1] = 0.10, what mean-reversion speed kappa is implied?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4705Stochastic Vol Diagnostic 15Before choosing a stochastic-vol model, what should you ask first about the empirical smile behavior you want to capture?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4707Stochastic Vol Diagnostic 17If the long-run variance mean theta increases, what usually happens to long-dated variance expectations?数理金融中等essay未尝试面试订阅