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4629Replication Scenario 14Why does the Black-Scholes replication story lean so heavily on market completeness?数理金融中等essay未尝试面试订阅4631Replication Sensitivity 16Why does making the binomial time step smaller make the replication route feel closer to continuous Black-Scholes hedging?数理金融中等essay未尝试面试订阅4633Higher rateIf the risk-free rate rises while the state payoffs stay the same, which piece of the one-step replicating portfolio is directly affected even before the hedge ratio changes?数理金融中等essay未尝试面试订阅4634Replication Sensitivity 17Why does adding more binomial steps usually make backward induction more informative about dynamic hedging rather than less?数理金融中等essay未尝试面试订阅4638Before using qBefore introducing risk-neutral probabilities inside the replication route, what more primitive object should you already have in hand?数理金融中等essay未尝试面试订阅4639Before discussing completenessWhat should you inspect first before saying replication will produce a unique price?数理金融中等essay未尝试面试订阅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