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2096Infer Event-Window Length From a Fair Variance Strike 1A 252-day variance swap assumes instantaneous volatility 0.4 during an event window of unknown length d trading days and volatility 0.2 during the remaining days. If the annualized fair volatility strike is 0.3, approximately how many trading days does the event window last?数理金融简单数值题未尝试免费2101Recover the Missing Log Return From a Variance Fixing 6A variance-swap fixing uses RV = (252/n) * sum r i 2 with n=4. Three logged returns have already been recorded: [0.01, -0.02, 0.015]. What absolute missing return |r 4| would make the realized variance equal 0.04725?数理金融简单数值题未尝试免费2104Recover the Missing Log Return From a Variance Fixing 9A variance-swap fixing uses RV = (252/n) * sum r i 2 with n=4. Three logged returns have already been recorded: [0.012, 0.011, -0.009]. What absolute missing return |r 4| would make the realized variance equal 0.024885?数理金融简单数值题未尝试免费2105Recover the Missing Log Return From a Variance Fixing 10A variance-swap fixing uses RV = (252/n) * sum r i 2 with n=4. Three logged returns have already been recorded: [0.015, -0.005, -0.012]. What absolute missing return |r 4| would make the realized variance equal 0.045234?数理金融简单数值题未尝试免费2106Infer Remaining Flat Volatility From a Live Variance Mark 11A variance swap has observed 30 trading days out of 90. Realized variance so far is 0.035, and the current fair full-life variance strike is 0.038333. If the remaining window is assumed to carry one flat volatility level, what annualized volatility does that imply for the remaining life?数理金融中等数值题未尝试面试订阅2111Infer Stress Probability From a Variance Forecast 16A one-year variance forecast says annualized volatility will be 0.15 in a calm regime and 0.35 in a stress regime. If the fair variance-swap volatility strike is 0.24, what risk-neutral probability of the stress regime is implied by the variance forecast?数理金融中等数值题未尝试面试订阅2116Variance-Swap Surface Intuition 21Two one-year equity option surfaces have the same ATM implied volatility, but Surface B has much more expensive downside puts than Surface A. Why can Surface B still imply a meaningfully higher fair variance-swap strike?数理金融困难essay未尝试面试订阅2117Variance-Swap Sampling Intuition 22A quarter has only two very large overnight gap moves and otherwise tiny close-to-close returns. Why can realized variance still end up far above what a smooth diffusion intuition would suggest?数理金融困难essay未尝试面试订阅2118Variance-Swap Modeling Intuition 23Why can simple-return and log-return fixing conventions differ materially once moves become large?数理金融困难essay未尝试面试订阅2119Variance-Swap Modeling Intuition 24Why can a variance swap mark-to-market move even if the headline implied-vol surface looks unchanged at first glance?数理金融困难essay未尝试面试订阅2120Variance-Swap Modeling Intuition 25Why does a capped variance swap usually trade cheaper than an uncapped one with the same strike?数理金融困难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