题目5663 · 数理金融
Why Discounting Still Matters In Simulation
Why is it incorrect to average terminal payoffs from a risk-neutral simulation and stop there without discounting?
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中文题目题目5515 · 金融与交易
Why Multi-Round Policies Need Simulation
Why is backtesting a multi-round quoting policy usually more naturally done path by path instead of only through average per-quote metrics?
打开 →题目2391 · 数学
95% Half-Width From Sample Volatility and Path Count 21
A Monte Carlo estimator has sample standard deviation 5 across n=400 paths. Using the normal approximation, what is the 95% half-width?
打开 →题目2394 · 数学
Confidence Interval From Mean and Standard Error 24
A Monte Carlo estimate is 12.0 with standard error 0.4. Using the normal approximation, what 95% confidence interval do you report?
打开 →题目2373 · 数学
Infer Antithetic Correlation From the Variance Ratio 3
A payoff is averaged with its antithetic partner. The variance of the antithetic average is 30% of the crude single-path variance, and the two legs have equal variance. What correlation rho is implied between the paired payoffs?
打开 →题目2371 · 数学
Infer Covariance From an Optimal Control Weight 1
A control variate Y has Var(Y)=16. The desk estimates the optimal coefficient b*=0.75 in X-b(Y-E[Y]). What Cov(X,Y) is implied?
打开 →题目2386 · 数学
Infer Regime Probability From Conditional Means 16
A payoff has conditional mean 5 in a calm regime and -2 in a stress regime. The unconditional mean is 2.2. What calm-regime probability is implied?
打开 →题目4886 · 数理金融
Infer Second-Stratum Volatility From Target Neyman Share 21
Two strata have population weights N1=0.6 and N2=0.4. Their standard deviations are sigma1=2 and sigma2=unknown. Under equal-cost Neyman allocation, the desk wants stratum 2 to receive 50% of the samples. What sigma2 is implied?
打开 →题目2372 · 数学
Infer the Known Control Mean From the Adjusted Estimate 2
A raw Monte Carlo estimator has sample mean Xbar=9. The control sample mean is Ybar=41, the desk uses b*=0.5, and the adjusted estimate Xbar-b(Ybar-mu_Y) equals 8. What known control mean mu_Y is implied?
打开 →题目4888 · 数理金融
Infer Variance Ratio From Equal Neyman Shares 23
Two strata have population weights N1=0.7 and N2=0.3. Under equal-cost Neyman allocation they end up with equal sample shares. What ratio sigma2/sigma1 is implied?
打开 →题目2383 · 数学
Law of Total Variance in a Regime Simulator 13
What two pieces make up Var(X) under the law of total variance when a simulator first samples a regime Z and then samples X conditional on Z?
打开 →题目2376 · 数学
Paired-Difference Standard Error 6
Two pricing engines are compared with common random numbers. The paired differences have sample standard deviation s_D=2.8 across n=49 shared paths. What is the standard error of the estimated mean difference?
打开 →题目2382 · 数学
Remaining Variance Fraction Under Pairing 12
Without common random numbers, two independent estimators have standard deviations 4 and 5, so the variance of their difference is 4^2+5^2. With pairing, the observed paired-difference standard deviation is 3. What fraction of the unpaired difference variance remains?
打开 →题目2392 · 数学
Required Paths for a Target Standard Error 22
A crude estimator has standard deviation 6. How many paths are needed to bring the standard error down to 0.3?
打开 →题目2377 · 数学
Required Shared Paths for a Half-Width Target 7
A common-random-numbers comparison has paired-difference standard deviation s_D=3.5. Using a 95% normal half-width target of 0.49, about how many shared paths are needed?
打开 →题目2393 · 数学
RMSE of an Unbiased Monte Carlo Estimate 23
An unbiased estimator has standard deviation 4 over one path and uses n=64 independent paths. What is the RMSE of the sample mean?
打开 →题目4889 · 数理金融
Three-Stratum Neyman Share 24
Three strata have population weights 0.5, 0.3, and 0.2, with standard deviations 1, 2, and 3. Under equal-cost Neyman allocation, what sample share should the third stratum receive?
打开 →题目4887 · 数理金融
Updated Neyman Share After a Volatility Change 22
Two equal-size strata each have population weight 0.5. After a shock, sigma1 rises to 2 while sigma2 stays at 1.5. Under equal-cost Neyman allocation, what sample share should stratum 1 now receive?
打开 →题目4890 · 数理金融
Updated Small-Stratum Share After Tail Risk Doubles 25
Two strata have population weights 0.8 and 0.2. The first stratum has sigma1=1. The second stratum's standard deviation jumps from 4 to 8. Under equal-cost Neyman allocation, what sample share should the second stratum now receive?
打开 →题目2379 · 数学
Variance Formula for an Antithetic Average 9
If X and X' have the same variance sigma^2 and correlation rho, what is Var((X+X')/2)?
打开 →题目2385 · 数学
When a Control Variate Can Make Things Worse 15
Why can a badly chosen control coefficient increase variance instead of reducing it?
打开 →题目2380 · 数学
Why a Stratified Estimator Is Unbiased 10
Why is the weighted sum of unbiased within-stratum sample means unbiased for the overall expectation?
打开 →题目2390 · 数学
Why Antithetics May Fail on a Highly Nonmonotone Payoff 20
Why can antithetic pairing fail to reduce variance for a payoff that oscillates strongly across the state space?
打开 →题目2395 · 数学
Why Bias Still Matters Alongside Variance 25
Why is a low-variance Monte Carlo estimator still problematic if it is biased?
打开 →题目2378 · 数学
Why Common Random Numbers Help Comparisons 8
Why can common random numbers reduce the variance of the difference between two estimators even if each estimator on its own is unchanged?
打开 →题目2710 · 机器学习
Why CPCV Helps but Does Not Solve Adaptive Idea Generation
Why can combinatorial pathwise validation improve robustness checks without fully solving the problem of researchers inventing new ideas after seeing the old results?
打开 →题目2387 · 数学
Why Importance Sampling Stays Unbiased 17
Why does reweighting by the likelihood ratio keep an importance-sampling estimator unbiased for the original expectation?
打开 →题目2388 · 数学
Why Rare Events Cause Huge Monte Carlo Noise 18
Why can a rare-event payoff have an unstable Monte Carlo estimate even when most simulated paths look harmless?
打开 →题目2389 · 数学
Why Regime Averaging Can Beat Crude Mixing 19
Why can separately estimating conditional means by regime and then averaging them outperform one crude pooled Monte Carlo run?
打开 →题目2384 · 数学
Why Regime Conditioning Can Reduce Variance 14
Why can conditioning on a regime variable before sampling payoffs reduce Monte Carlo variance?
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