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4448Correlation Shock Benefit 8An equal-weight composite combines two standardized signals. If their correlation drops from 0.6 to 0.2, by how much does the composite standard deviation fall?机器学习中等数值题未尝试面试订阅4449Target Alpha Weight 9A fast signal has expected alpha 9 bps and a slow signal has expected alpha 3 bps. In a composite C = w fast + (1-w) slow, what weight on the fast signal produces expected alpha 6.6 bps?机器学习中等数值题未尝试面试订阅4450MSE Gain From A Diversifying Forecast 10Forecast error variance is 4 for model A, 9 for model B, and their error covariance is 1. You blend them equally. By how much does the blended forecast's MSE improve relative to using model A alone?机器学习中等数值题未尝试面试订阅4456Higher CorrelationIf pairwise correlation between signals rises while their standalone quality stays unchanged, what usually happens to the diversification benefit of combining them?机器学习中等essay未尝试面试订阅4457Weight InstabilityIf estimated optimal combination weights jump around from month to month, what is the usual case for shrinkage?机器学习中等essay未尝试面试订阅4458More Signals, Same DataIf you keep adding candidate signals without increasing data length, what often happens to the reliability of estimated combination weights?机器学习中等essay未尝试面试订阅4459Score Scale DriftIf one signal's score scale drifts over time while another remains stable, what usually happens to a fixed raw-score blend?机器学习中等essay未尝试面试订阅4460Slow Signal WeightIf transaction costs rise materially, what usually happens to the appeal of slower-moving signals in the blend?机器学习中等essay未尝试面试订阅4606Higher dividend yieldIf the continuous dividend yield rises while spot, strike, volatility, and maturity stay fixed, what happens to the stock-leg term S0 e (-qT) N(d1) in the martingale derivation?数理金融中等essay未尝试面试订阅4607Longer maturityWhy does longer maturity usually make the martingale derivation more sensitive to the difference between the stock leg and the discounted strike leg?数理金融中等essay未尝试面试订阅4608Higher volatilityIn the martingale derivation, why does higher volatility usually help a call even though the discounted expected stock price itself does not change?数理金融中等essay未尝试面试订阅4609Forward price unchangedIf two markets have the same forward price but different pairs of (r,q), why can the martingale derivation still give different call values?数理金融中等essay未尝试面试订阅4610Higher strikeIf strike increases while everything else stays fixed, which term in the martingale call decomposition is most directly pushed up?数理金融中等essay未尝试面试订阅4631Replication Sensitivity 16Why does making the binomial time step smaller make the replication route feel closer to continuous Black-Scholes hedging?数理金融中等essay未尝试面试订阅4633Higher rateIf the risk-free rate rises while the state payoffs stay the same, which piece of the one-step replicating portfolio is directly affected even before the hedge ratio changes?数理金融中等essay未尝试面试订阅4634Replication Sensitivity 17Why does adding more binomial steps usually make backward induction more informative about dynamic hedging rather than less?数理金融中等essay未尝试面试订阅4641Break-Even Realized Vol From Hedging P&L 1A delta-hedged long option has gamma 0.04, spot 100, implied volatility 0.2, and hedge horizon 0.083 years. Over that horizon, the diffusion-style hedging P&L attributable to volatility mismatch is observed to be 0.6374 using the approximation 0.5*Gamma*S 2*(sigma real 2 - sigma imp 2)*dt. What realized volatility sigma real is implied?数理金融中等数值题未尝试面试订阅4642Break-Even Realized Vol From Hedging P&L 2A delta-hedged long option has gamma 0.03, spot 80, implied volatility 0.25, and hedge horizon 0.167 years. Over that horizon, the diffusion-style hedging P&L attributable to volatility mismatch is observed to be -0.4826 using the approximation 0.5*Gamma*S 2*(sigma real 2 - sigma imp 2)*dt. What realized volatility sigma real is implied?数理金融中等数值题未尝试面试订阅4651Assumption Breakdown Scenario 11Observed index options suddenly show a much steeper downside skew after crash fear rises. Which Black-Scholes assumption is being stressed most directly?数理金融中等essay未尝试面试订阅4652Assumption Breakdown Scenario 12Why do jumps create a particularly sharp failure mode for Black-Scholes delta hedging?数理金融中等essay未尝试面试订阅