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4716Admissible Higher-Strike Call Interval 1A call with strike 80 trades at 25. Ignoring discounting and using only no-arbitrage monotonicity and slope bounds across strikes, what admissible price interval does that imply for the call with higher strike 90?数理金融简单数值题未尝试面试订阅4718Admissible Higher-Strike Call Interval 3A call with strike 100 trades at 10.5. Ignoring discounting and using only no-arbitrage monotonicity and slope bounds across strikes, what admissible price interval does that imply for the call with higher strike 110?数理金融简单数值题未尝试面试订阅4721Butterfly Repair Or Ceiling 6For equally spaced strikes 90, 100, 110, call prices at the wings are C(90)=18.2 and C(110)=8.1. What is the largest arbitrage-free value the middle call C(100) can take under butterfly convexity?数理金融中等数值题未尝试面试订阅4722Butterfly Repair Or Ceiling 7For equally spaced strikes 80, 100, 120, call prices at the wings are C(80)=26 and C(120)=7. What is the largest arbitrage-free value the middle call C(100) can take under butterfly convexity?数理金融中等数值题未尝试面试订阅4723Butterfly Repair Or Ceiling 8For equally spaced strikes 95, 100, 105, calls trade at 14, 12.5, and 10. By how much must the middle call price be reduced to remove the butterfly arbitrage?数理金融中等数值题未尝试面试订阅4724Butterfly Repair Or Ceiling 9For equally spaced strikes 85, 95, 105, calls trade at 20, 14.8, and 10.5. How much could the middle call price rise before butterfly convexity is first violated?数理金融中等数值题未尝试面试订阅4725Butterfly Repair Or Ceiling 10For equally spaced strikes 100, 110, 120, calls trade at 11.5, 8.4, and 5.8. How much could the middle call price rise before butterfly convexity is first violated?数理金融中等数值题未尝试面试订阅4726Calendar Repair Size 11At one strike, the shorter-maturity call with T=0.5 trades at 8.2 and the longer-maturity call with T=1 trades at 9.4. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4727Calendar Repair Size 12At one strike, the shorter-maturity call with T=1 trades at 11 and the longer-maturity call with T=2 trades at 12.8. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4728Calendar Repair Size 13At one strike, the shorter-maturity call with T=0.25 trades at 5.1 and the longer-maturity call with T=0.75 trades at 5. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4729Calendar Repair Size 14At one strike, the shorter-maturity call with T=0.5 trades at 7.5 and the longer-maturity call with T=1.5 trades at 10.2. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4730Calendar Repair Size 15At one strike, the shorter-maturity call with T=1 trades at 9.8 and the longer-maturity call with T=3 trades at 9.6. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4731Surface Arbitrage Scenario 16Why is butterfly arbitrage usually interpreted as a sign of a negative implied density somewhere?数理金融中等essay未尝试面试订阅4732Surface Arbitrage Scenario 17Why do desks clean or smooth option surfaces before using them in local-vol or risk systems?数理金融中等essay未尝试面试订阅4733Surface Arbitrage Scenario 18Why is a surface being static-arbitrage-free still not enough to guarantee realistic smile dynamics?数理金融中等essay未尝试面试订阅4734Surface Arbitrage Scenario 19If you detect a tiny local butterfly violation caused by noisy quotes, what is usually the first practical response?数理金融中等essay未尝试面试订阅4735Surface Arbitrage First Step 20Before fitting a model to an implied-vol surface, what should you inspect first?数理金融中等essay未尝试面试订阅4736Surface Arbitrage First Step 21Before repairing a quote, what should you identify first about the violation?数理金融中等essay未尝试面试订阅4737Surface Arbitrage First Step 22Before calling a quote 'wrong,' what data-quality question should you ask first?数理金融中等essay未尝试面试订阅4738Surface Arbitrage First Step 23Before using convexity across strikes, what structural condition should you check first about strike spacing?数理金融中等essay未尝试面试订阅