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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4591Martingale Carry Inference 1Spot is 100, maturity is 1 year, and the prepaid forward price is 97.0446. What continuous dividend yield q is implied?数理金融简单数值题未尝试面试订阅4592Martingale Carry Inference 2Spot is 80, maturity is 1 year, the forward price is 82.4364, and the risk-free rate is 5%. What continuous dividend yield q is implied?数理金融简单数值题未尝试面试订阅4593Martingale Carry Inference 3A stock has spot 90 and 1-year discounted risk-neutral expectation E[e -rT S T] = 88.218. What continuous dividend yield q is implied?数理金融简单数值题未尝试面试订阅4594Martingale Carry Inference 4Under risk-neutral pricing, spot is 120, risk-free rate is 4%, dividend yield is 1.5%, and maturity is 2 years. What is E[S T]?数理金融简单数值题未尝试面试订阅4595Martingale Carry Inference 5A 1-year prepaid forward on a stock is 96, and the corresponding forward price is 100.9221. What risk-free rate r is implied?数理金融简单数值题未尝试面试订阅4596Martingale Decomposition Arithmetic 6In the martingale decomposition of a call, the discounted share-side term is 38.2 and the call value is 6.8. What discounted strike-side term must be subtracted?数理金融中等数值题未尝试面试订阅4597Martingale Decomposition Arithmetic 7A call price is 5.4 and the discounted strike-side term K e -rT N(d2) is 24.2. What discounted share-side term S0 e -qT N(d1) is implied?数理金融中等数值题未尝试面试订阅4598Martingale Decomposition Arithmetic 8The prepaid forward is 48.5, the call price is 7.3, and the discounted strike is 50.1. What put price follows from put-call parity?数理金融中等数值题未尝试面试订阅4599Martingale Decomposition Arithmetic 9In a call decomposition, the discounted asset-side tail expectation is 44.1 and the discounted strike-side tail expectation is 35.7. What call value follows?数理金融中等数值题未尝试面试订阅4600Martingale Decomposition Arithmetic 10A call is worth 6.2, a put is worth 4.7, and the discounted strike is 51.5. What prepaid forward price is implied by put-call parity?数理金融中等数值题未尝试面试订阅4601Martingale Scenario 11Why do d1 and d2 appear as two different normal arguments in the martingale derivation of a Black-Scholes call?数理金融中等essay未尝试面试订阅4602Martingale Scenario 12Why is discounted pricing central in the martingale derivation rather than a cosmetic last step?数理金融中等essay未尝试面试订阅4603Martingale Scenario 13Why should the martingale route and the PDE route give the same Black-Scholes price?数理金融中等essay未尝试面试订阅4604Martingale Scenario 14Why does a continuous dividend yield enter the martingale derivation before the final formula is written down?数理金融中等essay未尝试面试订阅4605Martingale First Step 15Before carrying out any lognormal integral in the martingale derivation, what object should you isolate first?数理金融中等essay未尝试面试订阅