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4507Why a Redundant Asset Does Not Collapse a Pricing IntervalIn an incomplete market, why does listing one more asset fail to eliminate price intervals if that asset's payoff lies in the old span?数理金融中等essay未尝试面试订阅4508Why an Incomplete Market Can Still Uniquely Price One ClaimWhy can a market be globally incomplete yet still assign a unique arbitrage-free price to one particular claim?数理金融中等essay未尝试面试订阅4509Why Strict Positivity Matters When Talking About Equivalent MeasuresWhy is strict positivity of state prices or implied probabilities part of the theorem's language rather than a cosmetic side condition?数理金融中等essay未尝试面试订阅4510Why Uniqueness of the Pricing Measure and Completeness Tell the Same Geometry StoryAt interview level, why should you think of 'unique martingale measure' and 'complete market' as two views of the same linear-algebra fact?数理金融中等essay未尝试面试订阅4511Why Price Intervals Come from Missing DirectionsWhy do arbitrage-free price intervals typically appear when the traded span misses some state-space directions?数理金融中等essay未尝试面试订阅4512What to Challenge First When Someone Says 'Three Securities, Three States, So Complete'A PM says 'there are three securities and three states, so the market is complete.' What is the first structural check you should push back with?数理金融中等essay未尝试面试订阅4513Why Attainability Comes Before Probability LanguageIf a nontraded claim seems to have several candidate prices, what should you verify before arguing about which probability measure is 'correct'?数理金融中等essay未尝试面试订阅4514Why the Same Market Can Have One Price for Replicable Claims and Many for OthersHow can one and the same market produce exact single prices for some claims and only intervals for others without contradiction?数理金融中等essay未尝试面试订阅4515Why an Extra Asset Must Add a New Direction, Not Just a New StoryWhen someone claims a newly listed security 'should help complete the market,' what makes that statement true or false?数理金融中等essay未尝试面试订阅4516Protected Half-Participation Note 1What static portfolio replicates the payoff 95 + 0.5*min((S T-100) +, 20)?数理金融简单essay未尝试面试订阅4517Stock With Upside Fee Cap 2What static portfolio replicates the payoff S T - min((S T-105) +, 15)?数理金融简单essay未尝试面试订阅4518Downside Floor On Fractional Stock 3What static portfolio replicates the payoff max(100, 0.8 S T)?数理金融简单essay未尝试面试订阅4519Shifted Stock With Cap 4What static portfolio replicates the payoff min(110, S T + 10)?数理金融简单essay未尝试面试订阅4521Bonus Corridor Note From a Verbal PayoffA note pays 100 if S T <= 100, then rises dollar-for-dollar with S T between 100 and 130, and is capped at 130 above that. Describe a static replication using bonds and vanilla options.数理金融中等essay未尝试面试订阅4522Soft Downside Deductible 7What static portfolio replicates the payoff 100 - min((90-S T) +, 10)?数理金融中等essay未尝试面试订阅4523Share Plus Cash Cap 8What static portfolio replicates the payoff 5 + min(S T, 105)?数理金融中等essay未尝试面试订阅4524Half Share With Floor 9What static portfolio replicates the payoff 0.5 S T + 0.5 max(S T, 100)?数理金融中等essay未尝试面试订阅4525Half-Participation Capped Upside NoteA structured note guarantees 100. Above S T = 120 it participates in 50% of upside until S T reaches 140, and above 140 no further upside is paid. What static replication matches this payoff?数理金融中等essay未尝试面试订阅4526Equity Participation With a Put CushionA payoff gives 90% of the stock value at maturity and, if the stock finishes below 100, adds 30% of the shortfall from 100. Describe a static replication with simple building blocks.数理金融中等essay未尝试面试订阅4527Two-Ramp Corridor PayoffA payoff is zero below 95, rises one-for-one with S T between 95 and 110, stays flat between 110 and 135, and then resumes rising one-for-one above 135. What static option portfolio replicates it?数理金融中等essay未尝试面试订阅