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4848Infer Explicit Update Weight 8A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=5, u up=6.5, u down=4.5, and u new=5.3. What lambda was used?数理金融简单数值题未尝试面试订阅4849Infer Explicit Update Weight 9A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=7, u up=8, u down=6.2, and u new=7.07. What lambda was used?数理金融简单数值题未尝试面试订阅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4851Infer Rate From Crank-Nicolson Off-Diagonals 11Under the common Black-Scholes Crank-Nicolson convention alpha i = 0.25*Delta t*(sigma 2*i 2 - r*i) and gamma i = 0.25*Delta t*(sigma 2*i 2 + r*i). A grid dump reports i=2, Delta t=0.5, alpha i=0.0125, and gamma i=0.0275. What risk-free rate r is implied?数理金融中等数值题未尝试面试订阅4856Call Upper BoundaryIn a finite-difference grid for a European call, why is the far-right boundary often set close to S max - K e (-rτ) rather than to a constant?数理金融困难essay未尝试面试订阅4857Put Lower BoundaryWhy does a European put grid often impose V(0,τ) ≈ K e (-rτ) at the left boundary?数理金融困难essay未尝试面试订阅4858Negative WeightsWhy are explicit or theta-scheme weights turning negative a warning sign for an option grid, especially near kinks?数理金融困难essay未尝试面试订阅4859Nonuniform GridWhy can clustering grid points around the strike improve gamma estimates more than simply extending S max farther out?数理金融困难essay未尝试面试订阅4860Too Small TruncationIf S max is chosen too low in a call-pricing grid, what directional bias do you expect for deep in-the-money call values near the top of the grid, and why?数理金融困难essay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4864Infer Coarse Estimate From Richardson Output 19A second-order finite-difference scheme uses Richardson extrapolation E R = (4E fine - E coarse)/3. If E R=10.6 and E fine=10.4, what coarse-grid estimate E coarse is implied?数理金融困难数值题未尝试面试订阅4865Infer Fine Estimate From Richardson Output 20A second-order finite-difference scheme uses Richardson extrapolation E R = (4E fine - E coarse)/3. If E R=2.8 and E coarse=2.4, what fine-grid estimate E fine is implied?数理金融困难数值题未尝试面试订阅4866Infer Antithetic Correlation From Variance Reduction 1A Monte Carlo desk averages each payoff with its antithetic partner. The variance of the antithetic average is observed to be 35% of the crude single-path variance. If the paired payoffs have equal variance, what correlation rho between the two payoffs is implied?数理金融简单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4876Paired-Difference Standard Error 11Two pricing algorithms are compared with common random numbers. The paired difference sample has standard deviation s D=3 across n=100 shared paths. What is the standard error of the estimated mean difference?数理金融中等数值题未尝试面试订阅