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2294LSM Implementation Judgment 14Why does time-step placement matter in LSM beyond just making the simulation mesh 'finer'?数理金融困难essay未尝试面试订阅2295LSM Implementation Judgment 15Why is 'more paths' not a complete answer if the continuation specification itself is misshapen?数理金融困难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2371Infer Covariance From an Optimal Control Weight 1A control variate Y has Var(Y)=16. The desk estimates the optimal coefficient b*=0.75 in X-b(Y-E[Y]). What Cov(X,Y) is implied?数学简单数值题未尝试免费2372Infer the Known Control Mean From the Adjusted Estimate 2A raw Monte Carlo estimator has sample mean Xbar=9. The control sample mean is Ybar=41, the desk uses b*=0.5, and the adjusted estimate Xbar-b(Ybar-mu Y) equals 8. What known control mean mu Y is implied?数学简单数值题未尝试免费2373Infer Antithetic Correlation From the Variance Ratio 3A payoff is averaged with its antithetic partner. The variance of the antithetic average is 30% of the crude single-path variance, and the two legs have equal variance. What correlation rho is implied between the paired payoffs?数学中等数值题未尝试免费2374Why the Control-Variate Estimator Is Unbiased 4Why is X-b(Y-E[Y]) unbiased for E[X] for any fixed constant b?数学中等derivation未尝试免费2375Why the Optimal Control Weight Equals Cov/Var 5Why does the variance-minimizing control weight satisfy b*=Cov(X,Y)/Var(Y)?数学困难derivation未尝试免费2376Paired-Difference Standard Error 6Two pricing engines are compared with common random numbers. The paired differences have sample standard deviation s D=2.8 across n=49 shared paths. What is the standard error of the estimated mean difference?数学简单数值题未尝试免费2377Required Shared Paths for a Half-Width Target 7A common-random-numbers comparison has paired-difference standard deviation s D=3.5. Using a 95% normal half-width target of 0.49, about how many shared paths are needed?数学中等数值题未尝试免费2378Why Common Random Numbers Help Comparisons 8Why can common random numbers reduce the variance of the difference between two estimators even if each estimator on its own is unchanged?数学中等derivation未尝试免费2379Variance Formula for an Antithetic Average 9If X and X' have the same variance sigma 2 and correlation rho, what is Var((X+X')/2)?数学中等derivation未尝试面试订阅2380Why a Stratified Estimator Is Unbiased 10Why is the weighted sum of unbiased within-stratum sample means unbiased for the overall expectation?数学困难derivation未尝试面试订阅2382Remaining Variance Fraction Under Pairing 12Without common random numbers, two independent estimators have standard deviations 4 and 5, so the variance of their difference is 4 2+5 2. With pairing, the observed paired-difference standard deviation is 3. What fraction of the unpaired difference variance remains?数学简单数值题未尝试免费2383Law of Total Variance in a Regime Simulator 13What two pieces make up Var(X) under the law of total variance when a simulator first samples a regime Z and then samples X conditional on Z?数学中等derivation未尝试免费2384Why Regime Conditioning Can Reduce Variance 14Why can conditioning on a regime variable before sampling payoffs reduce Monte Carlo variance?数学困难derivation未尝试面试订阅