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4499One New Direction Added to a 7-State Rank-5 MarketA market has 7 states and current traded-payoff rank 5. A newly listed asset is known to add one genuinely independent payoff direction. After adding it, how many more independent payoff directions are still needed to make the market complete?数理金融中等数值题未尝试面试订阅4501Claim Price Interval From State-Price Family 11A family of state-price vectors is pi(lambda) = (0.25+lambda, 0.50-2lambda, 0.20+lambda) with lambda constrained to [0, 0.05]. For the claim payoff (0,1,3), what arbitrage-free price interval does the family imply?数理金融中等数值题未尝试面试订阅4502How Many Candidate Claims Are Automatically Uniquely Priced? 1In a 4-state market, the traded span is generated by payoffs B0, B1, and B2. Three candidate claims are A = 2 B0 - B1, C = B1 + B2, and D = [1,0,0,0]. How many of A, C, and D are automatically guaranteed a unique arbitrage-free price from the traded market alone?数理金融中等数值题未尝试面试订阅4503How Many Candidate Claims Are Automatically Uniquely Priced? 2In a 5-state market, traded payoffs span H1, H2, and H3. Candidate claims are U = H1 + 2 H3, V = H2 - H1, and W = [0,1,0,0,0]. How many of U, V, and W are guaranteed uniquely priced just from attainability?数理金融中等数值题未尝试面试订阅4504How Many Candidate Claims Are Automatically Uniquely Priced? 3A market's traded span contains F0 and F1 but not the full state space. Candidate claims are M = 3 F0 - 0.5 F1, N = [1,0,1,0], and P = [0,1,0,1]. How many of M, N, and P are automatically guaranteed unique prices?数理金融中等数值题未尝试面试订阅4505How Many Candidate Claims Are Automatically Uniquely Priced? 4In a 4-state market, traded payoffs span G0, G1, and G2. Candidate claims are A = G0 + G1, B = 2 G2 - G1, C = G0 - G2, and D = [0,0,0,1]. How many of A, B, C, and D are guaranteed uniquely priced from the given information?数理金融中等数值题未尝试面试订阅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4528Capped Downside Insurance StripA protection strip pays nothing above 85, then increases dollar-for-dollar as S T falls from 85 to 70, but below 70 the protection is capped at 15. What static replication matches it?数理金融中等essay未尝试面试订阅4529Stock Plus Loss Cap 14What static portfolio replicates the payoff S T - (95-S T) + + (80-S T) +?数理金融中等essay未尝试面试订阅4530Cash Floor With Limited Upside ParticipationA product pays 92 if S T <= 100. Between 100 and 115 it rises with slope 0.7, and above 115 the payoff is capped. What static replication do you use?数理金融中等essay未尝试面试订阅