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2196Infer Flat Hazard From a Survival Probability 1In a reduced-form model with flat hazard lambda, the survival probability to time T is S(T)=exp(-lambda T). If T=1 and the observed survival probability is 0.980199, what lambda is implied?数理金融简单数值题未尝试免费2200Infer Flat Hazard From a Survival Probability 5In a reduced-form model with flat hazard lambda, the survival probability to time T is S(T)=exp(-lambda T). If T=1.5 and the observed survival probability is 0.913931, what lambda is implied?数理金融简单数值题未尝试免费2201Infer Hazard From a Zero-Recovery Credit Bond Quote 6Assume zero recovery and a flat hazard lambda. A defaultable zero-coupon bond has price P = exp(-(r+lambda)T). If r=0.03, T=2, and the quoted bond price is 0.904837, what lambda is implied?数理金融简单数值题未尝试免费2204Infer Hazard From a Zero-Recovery Credit Bond Quote 9Assume zero recovery and a flat hazard lambda. A defaultable zero-coupon bond has price P = exp(-(r+lambda)T). If r=0.015, T=0.75, and the quoted bond price is 0.951229, what lambda is implied?数理金融简单数值题未尝试免费2206Recover Recovery From the Credit Triangle 11Using the flat credit-triangle approximation spread ≈ lambda*(1-R), suppose the running spread is 0.03 and the flat hazard is 0.05. What recovery rate R is implied?数理金融简单数值题未尝试免费2211Forward Default Slice Between Two Dates 16A reduced-form model reports survival probabilities S(T1)=0.96 and S(T2)=0.9 with T2>T1. What conditional default probability over the interval (T1,T2], given survival to T1, is implied?数理金融中等数值题未尝试面试订阅2216Reduced-Form Credit Intuition 21Why do reduced-form models start from intensity rather than from a capital-structure barrier?数理金融困难essay未尝试面试订阅2217Reduced-Form Credit Intuition 22Why does 'recovery of par' differ conceptually from 'recovery of market value'?数理金融困难essay未尝试面试订阅2218Reduced-Form Credit Intuition 23Why does adding stochastic hazard usually introduce convexity into credit pricing?数理金融困难essay未尝试面试订阅2219Reduced-Form Credit Intuition 24Why does a steep survival curve often signal rising forward hazard rather than just 'more risk in total'?数理金融困难essay未尝试面试订阅2220Reduced-Form Credit Intuition 25Why are intensity models so natural for CDS calibration?数理金融困难essay未尝试面试订阅2221Infer Flat Hazard From a Par CDS Quote 1Under the flat-intensity approximation for a CDS, the par spread satisfies s ≈ lambda*(1-R). If the par spread is 0.018 and recovery is 0.4, what flat hazard lambda is implied?数理金融简单数值题未尝试免费2226Recover the Market CDS Spread From an Existing Position 6A protection buyer holds an existing CDS with contractual spread 0.01 and risky annuity RPV01 = 4.2. The buyer's mark-to-market is 0.0252 per unit notional under the linear approximation MTM ≈ (s mkt - c)*RPV01. What market spread s mkt is implied?数理金融简单数值题未尝试免费2227Recover the Market CDS Spread From an Existing Position 7A protection seller holds an existing CDS with contractual spread 0.015 and risky annuity RPV01 = 5. The seller's mark-to-market is 0.02 per unit notional under the linear approximation MTM ≈ (c - s mkt)*RPV01. What market spread s mkt is implied?数理金融简单数值题未尝试免费2229Recover the Market CDS Spread From an Existing Position 9A protection buyer holds an existing CDS with contractual spread 0.012 and risky annuity RPV01 = 2. The buyer's mark-to-market is -0.004 per unit notional under the linear approximation MTM ≈ (s mkt - c)*RPV01. What market spread s mkt is implied?数理金融简单数值题未尝试免费2231Recover Market Spread From an Upfront Quote 11A CDS has standard coupon 0.01, risky annuity RPV01 = 4, and upfront 0.16 per unit notional. Using the linear approximation upfront ≈ (s mkt - coupon)*RPV01, what market spread s mkt is implied?数理金融简单数值题未尝试免费2232Recover Risky Annuity From a CDS Quote 12A CDS has standard coupon 0.01 and market spread 0.032. Its quoted upfront is 0.11 per unit notional. Using upfront ≈ (s mkt - coupon)*RPV01, what RPV01 is implied?数理金融简单数值题未尝试免费2233Coupon Implied by an Observed Upfront 13A CDS market spread is 0.09 and RPV01 = 3.5. The desk observes an upfront of 0.14 per unit notional. Under upfront ≈ (s mkt - coupon)*RPV01, what coupon is implied?数理金融简单数值题未尝试免费2234Spread Gap Implied by Two Upfront Quotes 14Two CDS quotes use the same standard coupon 0.01 and the same RPV01 = 6. Their upfronts are 0.048 and 0.078 per unit notional. Under the linear approximation, what is the difference between their market spreads?数理金融简单数值题未尝试免费2235Coupon Needed for a Target Upfront 15A CDS has market spread 0.04 and risky annuity RPV01 = 4.8. What standard coupon would make the linearized upfront equal 0.024 per unit notional?数理金融简单数值题未尝试免费