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3766Half-Life of a Moderately Mean-Reverting SpreadAn OU deviation decays in mean like e (-kappa t) with kappa = 0.35. What is its half-life?随机过程中等derivation未尝试面试订阅3771Speed Implied by a 40% Gap After One YearIn an OU model, the expected deviation from the long-run mean shrinks by a factor 0.4 over 1 years. What kappa does this imply?随机过程中等derivation未尝试面试订阅3773Speed Implied by a 60% Gap After Half a YearIn an OU model, the expected deviation from the long-run mean shrinks by a factor 0.6 over 0.5 years. What kappa does this imply?随机过程中等derivation未尝试面试订阅3776Diffusion Strength from a Stationary Variance TargetAn OU process has mean-reversion speed kappa = 0.8 and stationary variance 0.5. What diffusion coefficient sigma is implied?随机过程中等derivation未尝试面试订阅3781Long-Run Mean from a One-Year Expected LevelAn OU process starts at X 0 = 8 and has mean-reversion speed kappa = 0.6. If E[X 1] = 5.6, what long-run mean theta is implied?随机过程中等derivation未尝试面试订阅3782Long-Run Mean from a Half-Year Reversion TargetAn OU process starts at X 0 = 2.5 and has mean-reversion speed kappa = 1.2. If the expected value at t = 0.5 is 1.4, what long-run mean theta is implied?随机过程中等derivation未尝试面试订阅3784Long-Run Mean from a Mid-Horizon ForecastAn OU process starts at X 0 = 1.5 and has mean-reversion speed kappa = 0.9. If E[X 1.5] = 2.1, what long-run mean theta is implied?随机过程中等derivation未尝试面试订阅3786Why OU Is Mean-Reverting but Brownian Motion Is NotWhat is the structural reason an OU process is mean-reverting while plain Brownian motion is not?随机过程中等essay未尝试面试订阅3787Why Half-Life Is a Better Summary Than One-Step DriftWhy do practitioners often summarize an OU process by half-life instead of by quoting the raw drift coefficient alone?随机过程中等essay未尝试面试订阅3788Why Stationary Variance Balances Sigma Against KappaWhy does the OU stationary variance depend on both sigma and kappa instead of on the diffusion coefficient alone?随机过程中等essay未尝试面试订阅3789Why a Large Kappa Can Hide a Large SigmaHow can an OU process have a large diffusion coefficient and still look tightly clustered around its mean?随机过程中等essay未尝试面试订阅3790Why OU Is Often a Better Spread Model Than a Random WalkWhy is OU often a more plausible model than a random walk for a spread that traders believe should revert?随机过程中等essay未尝试面试订阅6041One-Year Conditional Variance of an OU ProcessAn OU process has mean-reversion speed kappa = 0.5 and diffusion coefficient sigma = 0.3. Given X 0, what is the conditional variance Var(X 1 | X 0)?随机过程中等derivation未尝试面试订阅6042Long-Run Variance of a Mean-Reverting RateA short rate follows an OU process with kappa = 1.5 and sigma = 0.12. What is its long-run (stationary) variance?随机过程简单derivation未尝试面试订阅6043Autocorrelation of a Stationary OU Process at a LagA stationary OU process has mean-reversion speed kappa = 0.7. What is the autocorrelation between X t and X t+2 ?随机过程简单derivation未尝试面试订阅