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?
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中文题目题目5654 · 数理金融
Asian Path Payoff 4
A simulated path for an arithmetic-average Asian call is [95, 92, 90, 97] with strike 94. What payoff does this single path contribute to the Monte Carlo estimator?
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4866 · 数理金融
Infer Antithetic Correlation From Variance Reduction 1
A Monte Carlo desk averages each payoff with its antithetic partner. The variance of the antithetic average is observed to be 35% of the crude single-path variance. If the paired payoffs have equal variance, what correlation rho between the two payoffs is implied?
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4871 · 数理金融
Infer Covariance From Optimal Control Weight 6
A control variate Y has sample variance Var(Y)=25. The optimal control coefficient is estimated as b*=0.8 in the estimator X - b*(Y-E[Y]). What Cov(X,Y) is implied?
打开 →题目4872 · 数理金融
Infer Covariance From Optimal Control Weight 7
A control variate Y has sample variance Var(Y)=4. The desk estimates the optimal coefficient b*=1.5 in X - b*(Y-E[Y]). What Cov(X,Y) is implied?
打开 →题目4873 · 数理金融
Infer Covariance From Optimal Control Weight 8
A control variate Y has sample variance Var(Y)=9. The estimated optimal control coefficient is b*=-0.6. What Cov(X,Y) is implied?
打开 →题目4874 · 数理金融
Infer Known Control Mean From Adjusted Estimate 9
A raw Monte Carlo estimator has sample mean Xbar=12. The control sample mean is Ybar=103, the desk uses b*=0.5, and the adjusted estimate Xbar - b*(Ybar-mu_Y) equals 10.5. What known control mean mu_Y is implied?
打开 →题目4884 · 数理金融
Infer Missing Mid-Regime Mean In a Three-State Mixture 19
A payoff has regime probabilities 0.5, 0.3, and 0.2. The conditional means are 1, m, and -2, and the overall expected payoff is 0.7. What is m?
打开 →题目4882 · 数理金融
Infer Missing Stress Mean From Tower Equation 17
A payoff has conditional mean 5 in a calm regime and unknown mean m in a stress regime. The calm regime probability is 0.6 and the overall expected payoff is 2.6. What is m?
打开 →题目4885 · 数理金融
Infer Regime Exercise Probability From Overall Expectation 20
In regime A, which occurs with probability 0.4, an option pays 10 if exercised. In regime B, which occurs with probability 0.6, it pays 4 if exercised, and the regime-B exercise probability is 0.25. The overall expected payoff is 2.6. What exercise probability in regime A is impl
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4881 · 数理金融
Infer Regime Probability From Conditional Means 16
A payoff has conditional mean 4 in a calm regime and -3 in a stress regime. The overall expected payoff is 1.9. What probability of the calm regime 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4883 · 数理金融
Infer Stress Probability From Conditional Means 18
A payoff has conditional mean 2 in a normal regime and -4 in a stress regime. The overall expected payoff is 0.8. What probability of the stress regime 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2320 · 数理金融
Jump-Risk Trading Intuition 10
Why does the smile effect of jumps often decay with maturity more differently than the smile effect of plain stochastic volatility?
打开 →题目2316 · 数理金融
Jump-Risk Trading Intuition 6
Why is exact jump simulation straightforward once the jump count is sampled?
打开 →题目2317 · 数理金融
Jump-Risk Trading Intuition 7
Why can Monte Carlo variance explode for tail-heavy payoffs under jump-diffusion even if vanilla prices are stable?
打开 →题目2318 · 数理金融
Jump-Risk Trading Intuition 8
Why do positive and negative jumps change the volatility smile in different ways even if jump variance is the same?
打开 →题目2319 · 数理金融
Jump-Risk Trading Intuition 9
Why can a jump-risk model still be useful even if it does not fit every strike perfectly?
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2141 · 数理金融
LMM Desk Intuition 21
Why is drift freezing popular even when everyone knows it is an approximation?
打开 →题目2142 · 数理金融
LMM Desk Intuition 22
Where does drift freezing usually break down first?
打开 →题目2143 · 数理金融
LMM Desk Intuition 23
Why are Bermudan rates options materially harder than caplets in an LMM?
打开 →题目2144 · 数理金融
LMM Desk Intuition 24
Why is the terminal measure convenient for simulation even though product pricing may later be expressed under another measure?
打开 →题目2145 · 数理金融
LMM Desk Intuition 25
Why do market models often align better with desk quotations than generic state-variable models?
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