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2303Poisson Jump Calibration 3A jump-diffusion has Poisson intensity lambda = 1.1. Over what horizon T would the no-jump probability equal 0.57695?数理金融简单数值题未尝试免费2304Poisson Jump Calibration 4In a Poisson jump model, the expected number of jumps over horizon T is lambda*T. If lambda = 1.8 and T = 0.75 years, what is the expected jump count?数理金融简单数值题未尝试免费2305Poisson Jump Calibration 5A desk estimates that the expected number of jumps over the next 0.5 years is 0.6. Under a Poisson jump model with expected count lambda*T, what intensity lambda is implied?数理金融简单数值题未尝试免费2306Jump Variance Decomposition 1A simplified jump-diffusion desk decomposition writes total log-return variance over horizon T as sigma 2*T + lambda*T*delta 2. If sigma = 0.2, T = 1, lambda = 0.8, and total variance is 0.0884, what jump-size dispersion delta is implied?数理金融中等数值题未尝试面试订阅2307Jump Variance Decomposition 2Using total variance = sigma 2*T + lambda*T*delta 2, suppose sigma = 0.18, T = 0.5, delta = 0.12, and total variance is 0.027. What jump intensity lambda is implied?数理金融中等数值题未尝试面试订阅2308Jump Variance Decomposition 3A simplified jump-diffusion uses total variance = sigma 2*T + lambda*T*delta 2. If lambda = 1.2, T = 1, delta = 0.08, and total variance is 0.0624, what diffusion volatility sigma is implied?数理金融中等数值题未尝试面试订阅2310Jump Variance Decomposition 5Suppose total log-return variance over horizon T is modeled as sigma 2*T + lambda*T*delta 2. If sigma = 0.22, lambda = 1.1, delta = 0.09, and total variance is 0.03883, what horizon T is implied?数理金融中等数值题未尝试面试订阅2311Jump-Risk Trading Intuition 1Why do negative jumps create downside skew even when the diffusion part is symmetric?数理金融中等essay未尝试面试订阅2312Jump-Risk Trading Intuition 2Why can a Black-Scholes delta hedge look fine most days and still fail violently under jump risk?数理金融中等essay未尝试面试订阅2313Jump-Risk Trading Intuition 3Why are short-dated out-of-the-money options especially sensitive to jump assumptions?数理金融中等essay未尝试面试订阅2314Jump-Risk Trading Intuition 4Why can calibration struggle to distinguish jump frequency from jump size?数理金融中等essay未尝试面试订阅2315Jump-Risk Trading Intuition 5Why are jump models and stochastic-vol models complements rather than simple substitutes?数理金融中等essay未尝试面试订阅2316Jump-Risk Trading Intuition 6Why is exact jump simulation straightforward once the jump count is sampled?数理金融困难essay未尝试面试订阅2317Jump-Risk Trading Intuition 7Why can Monte Carlo variance explode for tail-heavy payoffs under jump-diffusion even if vanilla prices are stable?数理金融困难essay未尝试面试订阅2318Jump-Risk Trading Intuition 8Why do positive and negative jumps change the volatility smile in different ways even if jump variance is the same?数理金融困难essay未尝试面试订阅2319Jump-Risk Trading Intuition 9Why can a jump-risk model still be useful even if it does not fit every strike perfectly?数理金融困难essay未尝试面试订阅2320Jump-Risk Trading Intuition 10Why does the smile effect of jumps often decay with maturity more differently than the smile effect of plain stochastic volatility?数理金融困难essay未尝试面试订阅2400How Many Independent Fits to Hit a Variance TargetEach independently trained model has variance 2.4 and negligible bias. How many equally weighted independent fits must you average to bring the variance term below 0.3?机器学习中等derivation未尝试免费2403Variance of a Correlated Five-Model CommitteeFive models each have variance 1.6 and pairwise correlation 0.4. What is the variance of their equal-weight average?机器学习中等derivation未尝试免费2410Why Regularization Can Raise Train Error but Lower Test ErrorWhy is it perfectly consistent for regularization to worsen train fit but improve out-of-sample MSE?机器学习中等essay未尝试面试订阅