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4771Infer Current Short Rate From an Affine Bond Quote 6In an affine short-rate model, a zero-coupon bond is priced as P(0,T)=A(T)exp(-B(T)r0). For one maturity bucket the model exports A(T)=0.97, B(T)=2.5, and the bond quote is P(0,T)=0.899911. What current short rate r0 is implied?数理金融中等数值题未尝试面试订阅4773Infer Current Short Rate From an Affine Bond Quote 8In an affine short-rate model, a zero-coupon bond is priced as P(0,T)=A(T)exp(-B(T)r0). For one maturity bucket the model exports A(T)=0.94, B(T)=3, and the bond quote is P(0,T)=0.872079. What current short rate r0 is implied?数理金融中等数值题未尝试面试订阅4776CIR Positivity Cushion 11A desk wants to keep the CIR positivity condition just binding at 2*kappa*theta = sigma 2. If kappa=0.8 and theta=0.04, what is the largest volatility sigma that still satisfies the condition?数理金融中等数值题未尝试面试订阅4781Short-Rate Model Scenario Analysis 16A trader says, 'I only need today's short rate and one mean-reversion speed, so a short-rate model is good enough.' What key information about the yield curve is being compressed by that choice?数理金融中等essay未尝试面试订阅4782Short-Rate Model Scenario Analysis 17Why can a one-factor short-rate model still be useful for risk even though it cannot fit every yield-curve deformation exactly?数理金融中等essay未尝试面试订阅4783Short-Rate Model Scenario Analysis 18If your short-rate model frequently produces negative rates in a market where that is viewed as implausible, what is the practical modeling concern?数理金融中等essay未尝试面试订阅4784Short-Rate Model Scenario Analysis 19Why is calibrating only today's discount curve not enough to trust a short-rate model for option risk?数理金融中等essay未尝试面试订阅4785Short-Rate Model First Diagnostic 20Before picking a short-rate model, what should you check first about the products you need to price?数理金融中等essay未尝试面试订阅4786Short-Rate Model First Diagnostic 21Before using a one-factor mean-reverting model for curve risk, what empirical question should you ask first?数理金融中等essay未尝试面试订阅4787Short-Rate Model First Diagnostic 22If a short-rate calibration fits bonds but misses caps badly, what should you inspect first?数理金融中等essay未尝试面试订阅4788Short-Rate Model First Diagnostic 23Before treating negative simulated rates as acceptable, what should you verify first?数理金融中等essay未尝试面试订阅4789Short-Rate Model First Diagnostic 24Before comparing a short-rate model with HJM, what design tradeoff should you state first?数理金融中等essay未尝试面试订阅4790Short-Rate Model First Diagnostic 25Before concluding that the mean-reversion speed is 'too low,' what should you compare it with first?数理金融中等essay未尝试面试订阅4791Infer HJM Volatility From Forward Drift 1In a one-factor HJM setup with maturity gap tau=T-t=2, the desk observes an instantaneous forward drift alpha(t,T)=0.045 and assumes the volatility is constant across the bucket. Using alpha=sigma 2*tau, what sigma is implied?数理金融中等数值题未尝试面试订阅4792Infer HJM Volatility From Forward Drift 2In a one-factor HJM setup with maturity gap tau=T-t=1.5, the desk observes an instantaneous forward drift alpha(t,T)=0.06 and assumes the volatility is constant across the bucket. Using alpha=sigma 2*tau, what sigma is implied?数理金融中等数值题未尝试面试订阅4796Infer Integrated Volatility Mass In HJM 6At one maturity bucket, the desk estimates the endpoint instantaneous forward volatility sigma(t,T)=0.015 and the HJM no-arbitrage drift alpha(t,T)=0.027. In the one-factor relation alpha(t,T)=sigma(t,T)*integral t T sigma(t,u) du, what value is implied for integral t T sigma(t,u) du?数理金融中等数值题未尝试面试订阅4802HJM Scenario Analysis 12Why can HJM be more flexible than a short-rate model but harder to calibrate robustly?数理金融中等essay未尝试面试订阅4803HJM Scenario Analysis 13If two maturity buckets move very differently in the data, what does that suggest about a one-factor HJM specification?数理金融中等essay未尝试面试订阅4804HJM Scenario Analysis 14Why is fitting today's curve perfectly not enough to trust an HJM model for exotic rate options?数理金融中等essay未尝试面试订阅4806HJM First Diagnostic 16Before adding more HJM factors, what empirical check should you perform first?数理金融中等essay未尝试面试订阅