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4641Break-Even Realized Vol From Hedging P&L 1A delta-hedged long option has gamma 0.04, spot 100, implied volatility 0.2, and hedge horizon 0.083 years. Over that horizon, the diffusion-style hedging P&L attributable to volatility mismatch is observed to be 0.6374 using the approximation 0.5*Gamma*S 2*(sigma real 2 - sigma imp 2)*dt. What realized volatility sigma real is implied?数理金融中等数值题未尝试面试订阅4642Break-Even Realized Vol From Hedging P&L 2A delta-hedged long option has gamma 0.03, spot 80, implied volatility 0.25, and hedge horizon 0.167 years. Over that horizon, the diffusion-style hedging P&L attributable to volatility mismatch is observed to be -0.4826 using the approximation 0.5*Gamma*S 2*(sigma real 2 - sigma imp 2)*dt. What realized volatility sigma real is implied?数理金融中等数值题未尝试面试订阅4646Transaction Cost Breakeven 6A hedged option book expects to earn 60 of frictionless gamma/theta edge over the month. It will rebalance 40 times, with average absolute share turnover 120 shares per rebalance. What is the maximum per-share transaction cost that still leaves nonnegative expected net hedging P&L?数理金融简单数值题未尝试面试订阅4648Transaction Cost Breakeven 8A hedged option book expects to earn 37.5 of frictionless gamma/theta edge over the month. It will rebalance 25 times, with average absolute share turnover 200 shares per rebalance. What is the maximum per-share transaction cost that still leaves nonnegative expected net hedging P&L?数理金融简单数值题未尝试面试订阅4651Assumption Breakdown Scenario 11Observed index options suddenly show a much steeper downside skew after crash fear rises. Which Black-Scholes assumption is being stressed most directly?数理金融中等essay未尝试面试订阅4652Assumption Breakdown Scenario 12Why do jumps create a particularly sharp failure mode for Black-Scholes delta hedging?数理金融中等essay未尝试面试订阅4653Assumption Breakdown Scenario 13Why is 'we hedge daily' not a small implementation detail relative to Black-Scholes continuous hedging?数理金融中等essay未尝试面试订阅4654Assumption Breakdown Scenario 14Why can funding spreads and stock-borrow costs break the clean Black-Scholes replication logic even if volatility were truly constant?数理金融中等essay未尝试面试订阅4655Assumption Breakdown Diagnostic 15Before blaming every option-pricing error on volatility misspecification, what should you ask first?数理金融中等essay未尝试面试订阅4656Assumption Breakdown Diagnostic 16If you hedge more frequently, what usually happens to diffusion-style replication error and what usually happens to transaction costs?数理金融中等essay未尝试面试订阅4657Assumption Breakdown Diagnostic 17If jump risk becomes larger while diffusive volatility is unchanged, what happens to the credibility of a pure Black-Scholes delta hedge?数理金融中等essay未尝试面试订阅4658Assumption Breakdown Diagnostic 18If vol-of-vol rises materially, what usually happens to the plausibility of a single constant-volatility Black-Scholes description?数理金融中等essay未尝试面试订阅4659Assumption Breakdown Diagnostic 19If market liquidity deteriorates sharply, which Black-Scholes assumption becomes more dangerous to ignore?数理金融中等essay未尝试面试订阅4660Assumption Breakdown Diagnostic 20Why can longer-dated options expose Black-Scholes assumption failures more visibly than very short-dated options?数理金融中等essay未尝试面试订阅4661Assumption Breakdown Diagnostic 21Before using a gamma-PnL approximation, what should you check first about the hedge interval?数理金融中等essay未尝试面试订阅4662Assumption Breakdown Diagnostic 22Before concluding that transaction costs dominate the hedge result, what unit check should you do first?数理金融中等essay未尝试面试订阅4663Assumption Breakdown Diagnostic 23Before explaining an implied-vol skew by jumps, what should you distinguish first?数理金融中等essay未尝试面试订阅4664Assumption Breakdown Diagnostic 24Before saying discrete hedging error is the whole story, what comparison should you make first?数理金融中等essay未尝试面试订阅4665Assumption Breakdown Diagnostic 25Before declaring the model wrong, what convention check should you perform first?数理金融中等essay未尝试面试订阅