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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4841Minimum Stable Mesh Width 1For the transformed heat equation u t = nu*u xx, an explicit scheme uses lambda = nu*Delta t/Delta x 2 and requires lambda <= 0.5. If nu=0.04 and Delta t=0.125, what is the smallest Delta x that keeps the scheme stable?数理金融简单数值题未尝试面试订阅4846Infer Explicit Update Weight 6A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=8, u up=9, u down=11, and u new=9. What lambda was used?数理金融简单数值题未尝试面试订阅4847Infer Explicit Update Weight 7A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=10, u up=12, u down=9, and u new=10.4. What lambda was used?数理金融简单数值题未尝试面试订阅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