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4754Forward smile mattersWhy can two models fit today's smile similarly well and still disagree strongly on forward smile behavior?数理金融中等essay未尝试面试订阅4755First thing to askBefore arguing about the 'right' smile-dynamics convention, what should you ask first?数理金融中等essay未尝试面试订阅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5887Fair Variance Strike From a Discrete Option StripA one-year variance swap is replicated by a strip of OTM options. Using the Carr-Madan weighting w i = (ΔK / K i 2), the discount-adjusted strip values give sum i w i * price i = 0.0180 (in variance units before the 2/T scaling), and the linear forward-correction term contributes an additional 0.0020. With T = 1, the fair variance is K var = (2/T) * (strip + forward term). What is the fair annualized volatility strike (decimal)?数理金融中等数值题未尝试面试订阅5888Variance-Notional Swap SettlementA variance swap is quoted with a variance notional of 5,000 per variance point (where a variance point is one unit of 100*sigma 2, i.e. payoff = VarNotional * (10000*sigma realized 2 - 10000*K vol 2)). The volatility strike is K vol = 0.20 and realized annualized volatility over the life is 0.25. What is the payoff to the long (decimal/number)?数理金融简单数值题未尝试免费5889Vega Notional From Variance NotionalA trader wants a variance swap that behaves locally like a vega notional of 40,000 (per vol point) at the current volatility strike of K vol = 0.25. Using the standard linearization that near the strike the variance-notional payoff has vega notional N vega = 2 * K vol * N var (with vol points and variance both in decimal-consistent units), what variance notional N var should be set (number)?数理金融简单数值题未尝试免费5890Jump Contribution to Realized VarianceOver a 252-day window, 251 days each have a squared log-return of 0.0001, and a single jump day has a log-return of -0.10. Realized variance is annualized as RV = (252/252) * sum r i 2 (i.e. RV = sum of squared daily log-returns, since there are 252 observations). What annualized realized variance results, and what would it have been without the jump day (give both as decimals)?数理金融中等数值题未尝试面试订阅