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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4711Stochastic Vol Diagnostic 21Before calibrating a stochastic-vol model, what baseline should you compare it against first?数理金融中等essay未尝试面试订阅4712Stochastic Vol Diagnostic 22Before interpreting a fitted kappa economically, what data issue should you check first?数理金融中等essay未尝试面试订阅4714Stochastic Vol Diagnostic 24Before overfitting a stochastic-vol calibration, what should you ask first about the use case?数理金融中等essay未尝试面试订阅4715Stochastic Vol Diagnostic 25Before blaming the model for a poor fit, what should you check first about the quoted surface?数理金融中等essay未尝试面试订阅4716Admissible Higher-Strike Call Interval 1A call with strike 80 trades at 25. Ignoring discounting and using only no-arbitrage monotonicity and slope bounds across strikes, what admissible price interval does that imply for the call with higher strike 90?数理金融简单数值题未尝试面试订阅4718Admissible Higher-Strike Call Interval 3A call with strike 100 trades at 10.5. Ignoring discounting and using only no-arbitrage monotonicity and slope bounds across strikes, what admissible price interval does that imply for the call with higher strike 110?数理金融简单数值题未尝试面试订阅4721Butterfly Repair Or Ceiling 6For equally spaced strikes 90, 100, 110, call prices at the wings are C(90)=18.2 and C(110)=8.1. What is the largest arbitrage-free value the middle call C(100) can take under butterfly convexity?数理金融中等数值题未尝试面试订阅4722Butterfly Repair Or Ceiling 7For equally spaced strikes 80, 100, 120, call prices at the wings are C(80)=26 and C(120)=7. What is the largest arbitrage-free value the middle call C(100) can take under butterfly convexity?数理金融中等数值题未尝试面试订阅4723Butterfly Repair Or Ceiling 8For equally spaced strikes 95, 100, 105, calls trade at 14, 12.5, and 10. By how much must the middle call price be reduced to remove the butterfly arbitrage?数理金融中等数值题未尝试面试订阅4724Butterfly Repair Or Ceiling 9For equally spaced strikes 85, 95, 105, calls trade at 20, 14.8, and 10.5. How much could the middle call price rise before butterfly convexity is first violated?数理金融中等数值题未尝试面试订阅4725Butterfly Repair Or Ceiling 10For equally spaced strikes 100, 110, 120, calls trade at 11.5, 8.4, and 5.8. How much could the middle call price rise before butterfly convexity is first violated?数理金融中等数值题未尝试面试订阅