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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4708Stochastic Vol Diagnostic 18If spot-vol correlation becomes more negative, what usually happens to downside skew?数理金融中等essay未尝试面试订阅4709Stochastic Vol Diagnostic 19If vol-of-vol increases materially, what usually happens to uncertainty about future variance?数理金融中等essay未尝试面试订阅4710Stochastic Vol Diagnostic 20Why do stochastic-vol parameter differences often show up more clearly in longer-dated options than in very short-dated ones?数理金融中等essay未尝试面试订阅4741Sticky-Strike Versus Sticky-Moneyness 1Suppose the smile is parameterized in log-moneyness by sigma(k)= 0.2 + -0.12 k, with fixed strike K=110. Spot moves from 100 to 110. What implied volatility would the strike have under sticky-strike and under sticky-moneyness?数理金融中等数值题未尝试面试订阅4746Fixed-Strike Vol Shift 1With sigma(k)= 0.24 + -0.2 k in log-moneyness and fixed strike K=105, spot moves from 100 to 95. Under a sticky-moneyness convention, by how much does the fixed-strike implied volatility change?数理金融中等数值题未尝试面试订阅4751Why conventions matterWhy is saying 'the smile moved' incomplete unless you also say under which smile-dynamics convention you are describing it?数理金融中等essay未尝试面试订阅4752Why local vol criticism shows up hereWhy do practitioners often bring up local vol when discussing smile dynamics after spot moves?数理金融中等essay未尝试面试订阅4753Sticky delta intuitionWhat is the key intuition behind a sticky-delta style market description?数理金融中等essay未尝试面试订阅4754Forward smile mattersWhy can two models fit today's smile similarly well and still disagree strongly on forward smile behavior?数理金融中等essay未尝试面试订阅4755First thing to askBefore arguing about the 'right' smile-dynamics convention, what should you ask first?数理金融中等essay未尝试面试订阅