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2246State-Mixture Copula Calibration 1A desk uses a two-state one-factor copula toy model: conditional on a calm systemic state a name defaults with probability 0.40%, and conditional on a stress state it defaults with probability 6.40%. The unconditional one-year default probability is 1.60%. What stress-state probability is implied?数理金融中等数值题未尝试面试订阅2247State-Mixture Copula Calibration 2In a two-state conditional-independence model, a name has calm-state default probability 0.60% and stress-state weight 20.00%. If the unconditional one-year default probability is 2.40%, what stress-state default probability is implied?数理金融中等数值题未尝试面试订阅2248State-Mixture Copula Calibration 3A name's one-year default probability is modeled as a mixture of a calm state and a stress state. The stress-state probability is 25.00%, the stress-state default probability is 5.50%, and the unconditional default probability is 1.93%. What calm-state default probability is implied?数理金融中等数值题未尝试面试订阅2251Basket Dependence Recovery 1Two names have one-year default probabilities 2.00% and 3.00%. A desk prices a two-name first-to-default basket using a horizon first-to-default probability of 4.40%. What joint default probability over the horizon is implied?数理金融简单数值题未尝试免费2252Basket Dependence Recovery 2A two-name basket has first-to-default probability 3.10%. Name A has default probability 1.80%, and the desk's dependence model implies joint default probability 0.40%. What default probability for name B is implied?数理金融简单数值题未尝试免费2253Basket Dependence Recovery 3Two names have one-year default probabilities 1.20% and 2.50%. The desk's copula calibration implies joint default probability 0.30%. What first-to-default probability does that imply?数理金融简单数值题未尝试免费2256Copula Desk Intuition 1A junior trader says 'conditional independence means no dependence.' Why is that wrong in a one-factor copula?数理金融困难essay未尝试面试订阅2257Copula Desk Intuition 2Why can a senior tranche be more sensitive to stronger dependence even when the equity tranche barely moves?数理金融困难essay未尝试面试订阅2258Copula Desk Intuition 3Why does matching single-name spreads still leave a lot of freedom in basket-loss modeling?数理金融困难essay未尝试面试订阅2260Copula Desk Intuition 5Why is tail dependence really about bad states lining up, not just about average correlation looking high?数理金融困难essay未尝试面试订阅2261Copula Desk Intuition 6Why can a Gaussian copula fit one slice of quoted tranches and still be economically unconvincing?数理金融困难essay未尝试面试订阅2262Copula Desk Intuition 7Why do structured-credit desks still run scenario tables after calibrating a copula?数理金融困难essay未尝试面试订阅2263Copula Desk Intuition 8Why does sector concentration often break the spirit of a single-factor dependence model before the math breaks?数理金融困难essay未尝试面试订阅2264Copula Desk Intuition 9Why do attachment and detachment points turn a small change in dependence into a large change in tranche value?数理金融困难essay未尝试面试订阅2265Copula Desk Intuition 10Why can recovery assumptions and dependence assumptions interact instead of being separable knobs?数理金融困难essay未尝试面试订阅2266Copula Desk Intuition 11Why should a modeler distrust a dependence setup that implies a very benign calm regime and an absurdly catastrophic stress regime?数理金融中等essay未尝试面试订阅2267Copula Desk Intuition 12Why is nth-to-default risk more about ordering of losses than about one representative pairwise correlation?数理金融中等essay未尝试面试订阅2268Copula Desk Intuition 13Why is historical estimation of tail dependence usually much less reliable than historical estimation of calm-state default frequency?数理金融中等essay未尝试面试订阅2269Copula Desk Intuition 14Why is 'correlation smile' really a market symptom of model incompleteness rather than a literal smile of one primitive quantity?数理金融中等essay未尝试面试订阅2270Copula Desk Intuition 15Why do traders care whether a copula story is economically interpretable even if the day-one marks look fine?数理金融中等essay未尝试面试订阅