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4766Infer Long-Run Mean From a Vasicek Forecast 1A rates desk uses the Vasicek expectation formula E[r t] = theta + (r0-theta)e (-kappa t). It has r0=0.02, kappa=0.6931, and horizon t=1. The model forecast for E[r t] is 0.03. What long-run mean theta is implied?数理金融简单数值题未尝试面试订阅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