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2172Infer the Structural Default Put 2In a Merton-style structural view, firm assets are worth 95, the present value of promised debt is 75.5, and the observed equity value is 23. What risky debt value and what implied default put value on the assets are consistent with this decomposition?数理金融中等数值题未尝试面试订阅2173Infer the Structural Default Put 3In a Merton-style structural view, firm assets are worth 88, the present value of promised debt is 83.3, and the observed equity value is 9.4. What risky debt value and what implied default put value on the assets are consistent with this decomposition?数理金融中等数值题未尝试面试订阅2176Recover d2 From a Structural Default Probability 6In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 15.87% and you may use the standard-normal identity N(-1) = 0.1587. What d2 is implied?数理金融简单数值题未尝试免费2177Recover d2 From a Structural Default Probability 7In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 30.85% and you may use the standard-normal identity N(-0.5) = 0.3085. What d2 is implied?数理金融简单数值题未尝试免费2179Recover d2 From a Structural Default Probability 9In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 69.15% and you may use the standard-normal identity N(--0.5) = 0.6915. What d2 is implied?数理金融简单数值题未尝试免费2180Recover d2 From a Structural Default Probability 10In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 84.13% and you may use the standard-normal identity N(--1) = 0.8413. What d2 is implied?数理金融简单数值题未尝试免费2181Required Asset Cushion for a Target Distance to Default 11Using the simplified distance-to-default approximation DD = ln(A/F)/(sigma*sqrt(T)) and ignoring drift adjustments, what asset-to-face-value ratio A/F is needed to achieve DD = 1 when sigma = 0.2 and T = 1?数理金融中等数值题未尝试面试订阅2182Required Asset Cushion for a Target Distance to Default 12Using the simplified distance-to-default approximation DD = ln(A/F)/(sigma*sqrt(T)) and ignoring drift adjustments, what asset-to-face-value ratio A/F is needed to achieve DD = 1.5 when sigma = 0.25 and T = 0.5?数理金融中等数值题未尝试面试订阅2184Required Asset Cushion for a Target Distance to Default 14Using the simplified distance-to-default approximation DD = ln(A/F)/(sigma*sqrt(T)) and ignoring drift adjustments, what asset-to-face-value ratio A/F is needed to achieve DD = 1.2 when sigma = 0.15 and T = 2?数理金融中等数值题未尝试面试订阅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