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4850Infer Explicit Update Weight 10A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=4.5, u up=5.5, u down=4, and u new=4.6. What lambda was used?数理金融简单数值题未尝试面试订阅4861Infer Missing Upper Node From Delta 16At a stock grid with Delta S=5, the central-difference delta is approximated by Delta ≈ (V i+1 -V i-1 )/(2*Delta S). If V i-1 =12 and the desk wants Delta=0.8, what V i+1 is needed?数理金融中等数值题未尝试面试订阅4862Infer Center Node From Gamma 17At a stock grid with Delta S=2, the central-difference gamma is Gamma ≈ (V i+1 -2V i+V i-1 )/Delta S 2. If V i+1 =11, V i-1 =7, and the desk wants Gamma=0.5, what center value V i is needed?数理金融中等数值题未尝试面试订阅4863Infer Missing Lower Node From Delta 18At a stock grid with Delta S=1, the central-difference delta is Delta ≈ (V i+1 -V i-1 )/(2*Delta S). If V i+1 =9.4 and the target delta is 0.7, what V i-1 is implied?数理金融中等数值题未尝试面试订阅4871Infer Covariance From Optimal Control Weight 6A control variate Y has sample variance Var(Y)=25. The optimal control coefficient is estimated as b*=0.8 in the estimator X - b*(Y-E[Y]). What Cov(X,Y) is implied?数理金融中等数值题未尝试面试订阅4872Infer Covariance From Optimal Control Weight 7A control variate Y has sample variance Var(Y)=4. The desk estimates the optimal coefficient b*=1.5 in X - b*(Y-E[Y]). What Cov(X,Y) is implied?数理金融中等数值题未尝试面试订阅4873Infer Covariance From Optimal Control Weight 8A control variate Y has sample variance Var(Y)=9. The estimated optimal control coefficient is b*=-0.6. What Cov(X,Y) is implied?数理金融中等数值题未尝试面试订阅4874Infer Known Control Mean From Adjusted Estimate 9A raw Monte Carlo estimator has sample mean Xbar=12. The control sample mean is Ybar=103, the desk uses b*=0.5, and the adjusted estimate Xbar - b*(Ybar-mu Y) equals 10.5. What known control mean mu Y is implied?数理金融中等数值题未尝试面试订阅4896Translation-Invariant Capital Recovery 6A coherent capital rule reports rho(L-h)=4.6 after a deterministic hedge h=1.2 is added in every scenario. What was rho(L), and how much extra deterministic cash would still be needed to make the hedged position acceptable?数理金融简单数值题未尝试面试订阅4897Translation-Invariant Capital Recovery 7A book has coherent capital rho(L)=7.1. Treasury wants the post-cash capital to be 2.3. How large a deterministic cash injection is needed, and how much total deterministic cash would make the original book acceptable?数理金融简单数值题未尝试面试订阅4898Translation-Invariant Capital Recovery 8A desk starts with coherent capital rho(L)=4.4. After Treasury injects exactly enough deterministic cash to leave residual capital 0.9, how much cash was injected? If Treasury had injected only 3.0 instead, what residual capital would have remained?数理金融简单数值题未尝试面试订阅4899Translation-Invariant Capital Recovery 9The amount of deterministic capital needed to make a position acceptable is 3.9. After adding a guaranteed scenario-by-scenario recovery h, the coherent capital drops to 1.6. What recovery h was added?数理金融简单数值题未尝试面试订阅4900Translation-Invariant Capital Recovery 10A loss book has coherent capital 9.6. One deterministic hedge of size 1.8 is already in place. What residual capital remains? If the desk wants residual capital 5.0 instead, how much larger must the deterministic hedge be in total?数理金融简单数值题未尝试面试订阅4903Worst-Case Hedge Design 13Desk A has scenario losses [3, 2, 7, 1] and desk B has [1, 0, 2, 5]. Under rho(L)=max scenario loss, a hedge pays h only in scenario 3. What minimum h is needed so the combined capital becomes 6?数理金融中等数值题未尝试面试订阅4905Worst-Case Hedge Design 15Desk A has scenario losses [5, 3, 1, 4] and desk B has [1, 2, 0, 3]. Under rho(L)=max scenario loss, a hedge pays h only in scenario 4. What minimum h makes the combined capital drop from 7 to 6?数理金融中等数值题未尝试面试订阅4906Infer Worst Tail Loss From a Spectral Quote 16A spectral risk measure applies weights [0.1, 0.2, 0.3, 0.4] to ordered losses [1, 3, 5, x] from best to worst. If the reported spectral risk is 6.2, what worst ordered loss x is implied?数理金融中等数值题未尝试面试订阅4907Infer Worst Tail Loss From a Spectral Quote 17A spectral risk measure applies weights [0.05, 0.15, 0.3, 0.5] to ordered losses [0, 2, 4, x]. If the reported spectral risk is 7.1, what x is implied?数理金融中等数值题未尝试面试订阅4908Infer Worst Tail Loss From a Spectral Quote 18A spectral risk measure applies weights [0.2, 0.2, 0.25, 0.35] to ordered losses [1, 2, 6, x]. If the risk value is 5.6, what x is implied?数理金融中等数值题未尝试面试订阅4916Infer Normal Parameters From VaR And ES 1A desk assumes losses are normal with mean mu and standard deviation sigma. At alpha=0.95 it uses VaR = mu + z*sigma and ES = mu + k*sigma with z=1.645 and k=2.063. If the reported VaR is 7.58 and ES is 9.252, what are mu and sigma?数理金融中等数值题未尝试面试订阅4917Infer Normal Parameters From VaR And ES 2A normal-loss desk uses alpha=0.99 with VaR = mu + z*sigma and ES = mu + k*sigma, where z=2.326 and k=2.665. If VaR is 7.478 and ES is 8.495, what are mu and sigma?数理金融中等数值题未尝试面试订阅