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4611Martingale First Step 16Before invoking any theorem-level pricing statement in the martingale route, what should you identify first?数理金融中等essay未尝试面试订阅4612Martingale First Step 17What should you write down first before evaluating any tail expectation for a call payoff?数理金融中等essay未尝试面试订阅4613Martingale First Step 18Before interpreting d2 economically in the martingale derivation, what should you know first?数理金融中等essay未尝试面试订阅4696Fair Average Variance Over Horizon 6In a mean-reverting stochastic-vol model, variance starts at v0 = 0.04, long-run mean is theta = 0.09, mean-reversion speed is kappa = 1.5, and horizon is T = 1. What expected average variance E[(1/T)∫ 0 T v s ds] and annualized volatility sqrt of that average variance does the model imply?数理金融中等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4991Infer Missing Daily Move From Realized Variance Target 1A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three simple returns are 0.01, -0.02, and 0.015. What absolute fourth return |r 4| would make RV exactly equal the strike 0.04725, so the running payout is zero?金融与交易中等数值题未尝试面试订阅4992Infer Missing Daily Move From Realized Variance Target 2A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three simple returns are 0.008, -0.012, and 0.006. What absolute fourth return |r 4| would make RV exactly equal the strike 0.021672?金融与交易中等数值题未尝试面试订阅4993Infer Missing Daily Move From Realized Variance Target 3A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three returns are 0.02, -0.015, and 0.005. What absolute fourth return |r 4| makes RV exactly 0.04725?金融与交易中等数值题未尝试面试订阅4994Infer Missing Daily Move From Realized Variance Target 4A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three returns are 0.012, 0.011, and -0.009. What absolute fourth return |r 4| makes RV exactly 0.024885?金融与交易中等数值题未尝试面试订阅4995Infer Missing Daily Move From Realized Variance Target 5A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three returns are 0.015, -0.005, and -0.012. What absolute fourth return |r 4| makes RV exactly 0.045234?金融与交易中等数值题未尝试面试订阅4996Infer Forward Variance From Live Fair Strike 6A 90-day variance swap has observed 30 trading days. Realized variance so far is 0.035, and the current fair full-life variance strike is 0.038333333. What forward variance for the remaining 60 days is implied?金融与交易中等数值题未尝试面试订阅4997Infer Forward Variance From Live Fair Strike 7A 60-day variance swap has observed 20 trading days. Realized variance so far is 0.028, and the current fair variance strike is 0.030666667. What forward variance for the remaining life is implied?金融与交易中等数值题未尝试面试订阅4998Infer Forward Variance From Live Fair Strike 8A 120-day variance swap has observed 45 days. Realized variance so far is 0.05, and the live fair full-life strike is 0.045. What forward variance for the remaining 75 days is implied?金融与交易中等数值题未尝试面试订阅