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4756Bigger spot rallyIf the smile has negative slope in log-moneyness, what happens to the fixed-strike implied vol shift under sticky-moneyness when the spot rally becomes larger?数理金融中等essay未尝试面试订阅4757Bigger selloffWith a typical downside skew, what happens to fixed-strike implied vol under sticky-moneyness after a larger selloff?数理金融中等essay未尝试面试订阅4758Flatter smileIf the smile becomes flatter in log-moneyness, what happens to the difference between sticky-strike and sticky-moneyness for small spot moves?数理金融中等essay未尝试面试订阅4759Longer horizon dynamicsWhy can smile-dynamics convention differences matter more over longer horizons than over intraday moves?数理金融中等essay未尝试面试订阅4760More negative skewIf downside skew gets steeper, what usually happens to the sensitivity of fixed-strike vol to spot moves under sticky-moneyness?数理金融中等essay未尝试面试订阅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4831Rates Option Product Intuition 16Why is it useful to think of a cap as a strip of caplets before you worry about stochastic-rate models?数理金融中等essay未尝试面试订阅4832Rates Option Product Intuition 17Why does a payer swaption naturally benefit from higher future swap rates?数理金融中等essay未尝试面试订阅4833Rates Option Product Intuition 18Why does the annuity matter so much when discussing swaption payoff intuition?数理金融中等essay未尝试面试订阅4834Rates Option Product Intuition 19If a junior quant mixes up cap-floor parity with put-call parity on equities, what product-specific detail are they likely missing?数理金融中等essay未尝试面试订阅4835Rates Option First Diagnostic 20Before pricing a cap, what should you inspect first about the reset schedule?数理金融中等essay未尝试面试订阅4841Minimum Stable Mesh Width 1For the transformed heat equation u t = nu*u xx, an explicit scheme uses lambda = nu*Delta t/Delta x 2 and requires lambda <= 0.5. If nu=0.04 and Delta t=0.125, what is the smallest Delta x that keeps the scheme stable?数理金融简单数值题未尝试面试订阅4859Nonuniform GridWhy can clustering grid points around the strike improve gamma estimates more than simply extending S max farther out?数理金融困难essay未尝试面试订阅4860Too Small TruncationIf S max is chosen too low in a call-pricing grid, what directional bias do you expect for deep in-the-money call values near the top of the grid, and why?数理金融困难essay未尝试面试订阅4864Infer Coarse Estimate From Richardson Output 19A second-order finite-difference scheme uses Richardson extrapolation E R = (4E fine - E coarse)/3. If E R=10.6 and E fine=10.4, what coarse-grid estimate E coarse is implied?数理金融困难数值题未尝试面试订阅