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2096Infer Event-Window Length From a Fair Variance Strike 1A 252-day variance swap assumes instantaneous volatility 0.4 during an event window of unknown length d trading days and volatility 0.2 during the remaining days. If the annualized fair volatility strike is 0.3, approximately how many trading days does the event window last?数理金融简单数值题未尝试免费2101Recover the Missing Log Return From a Variance Fixing 6A variance-swap fixing uses RV = (252/n) * sum r i 2 with n=4. Three logged returns have already been recorded: [0.01, -0.02, 0.015]. What absolute missing return |r 4| would make the realized variance equal 0.04725?数理金融简单数值题未尝试免费2104Recover the Missing Log Return From a Variance Fixing 9A variance-swap fixing uses RV = (252/n) * sum r i 2 with n=4. Three logged returns have already been recorded: [0.012, 0.011, -0.009]. What absolute missing return |r 4| would make the realized variance equal 0.024885?数理金融简单数值题未尝试免费2105Recover the Missing Log Return From a Variance Fixing 10A variance-swap fixing uses RV = (252/n) * sum r i 2 with n=4. Three logged returns have already been recorded: [0.015, -0.005, -0.012]. What absolute missing return |r 4| would make the realized variance equal 0.045234?数理金融简单数值题未尝试免费2106Infer Remaining Flat Volatility From a Live Variance Mark 11A variance swap has observed 30 trading days out of 90. Realized variance so far is 0.035, and the current fair full-life variance strike is 0.038333. If the remaining window is assumed to carry one flat volatility level, what annualized volatility does that imply for the remaining life?数理金融中等数值题未尝试面试订阅2111Infer Stress Probability From a Variance Forecast 16A one-year variance forecast says annualized volatility will be 0.15 in a calm regime and 0.35 in a stress regime. If the fair variance-swap volatility strike is 0.24, what risk-neutral probability of the stress regime is implied by the variance forecast?数理金融中等数值题未尝试面试订阅2116Variance-Swap Surface Intuition 21Two one-year equity option surfaces have the same ATM implied volatility, but Surface B has much more expensive downside puts than Surface A. Why can Surface B still imply a meaningfully higher fair variance-swap strike?数理金融困难essay未尝试面试订阅2117Variance-Swap Sampling Intuition 22A quarter has only two very large overnight gap moves and otherwise tiny close-to-close returns. Why can realized variance still end up far above what a smooth diffusion intuition would suggest?数理金融困难essay未尝试面试订阅2118Variance-Swap Modeling Intuition 23Why can simple-return and log-return fixing conventions differ materially once moves become large?数理金融困难essay未尝试面试订阅2119Variance-Swap Modeling Intuition 24Why can a variance swap mark-to-market move even if the headline implied-vol surface looks unchanged at first glance?数理金融困难essay未尝试面试订阅2120Variance-Swap Modeling Intuition 25Why does a capped variance swap usually trade cheaper than an uncapped one with the same strike?数理金融困难essay未尝试面试订阅4666Inverse Spot From Affine Local Vol 1A local-vol surface is parameterized by sigma loc(S,t) = 0.2 + 0.12*(S/100 - 1). At what spot level S does the local volatility equal 0.212?数理金融简单数值题未尝试面试订阅4667Inverse Spot From Affine Local Vol 2A local-vol surface is parameterized by sigma loc(S,t) = 0.18 + -0.08*(S/80 - 1). At what spot level S does the local volatility equal 0.188?数理金融简单数值题未尝试面试订阅4671Regime Time Fraction From RMS Local Vol 6Along one realized path, local volatility equals 0.22 for a fraction f of the year and 0.3 for the rest. If the path-consistent RMS local volatility is observed to be 0.2709, what fraction f of the year was spent in the first regime?数理金融中等数值题未尝试面试订阅4676Local Vol Scenario 11Why can a local-vol model fit today's vanilla surface exactly while still generating unrealistic smile dynamics tomorrow?数理金融中等essay未尝试面试订阅4677Local Vol Scenario 12What does a local-vol model try to absorb into the state variable S that a stochastic-vol model would instead place into an extra state variable?数理金融中等essay未尝试面试订阅4678Local Vol Scenario 13Why does path dependence show up naturally when people criticize local-vol dynamics?数理金融中等essay未尝试面试订阅4679Local Vol Scenario 14Why is Dupire intuition often described as 'backing out an instantaneous local variance surface from vanilla prices'?数理金融中等essay未尝试面试订阅4680Local Vol Diagnostic 15Before trusting a local-vol calibration, what should you inspect first besides raw fit error?数理金融中等essay未尝试面试订阅4681Local Vol Diagnostic 16If sigma loc(S,t) slopes upward in S, what happens to local volatility after a spot rally in that model?数理金融中等essay未尝试面试订阅