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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2246State-Mixture Copula Calibration 1A desk uses a two-state one-factor copula toy model: conditional on a calm systemic state a name defaults with probability 0.40%, and conditional on a stress state it defaults with probability 6.40%. The unconditional one-year default probability is 1.60%. What stress-state probability is implied?数理金融中等数值题未尝试面试订阅2247State-Mixture Copula Calibration 2In a two-state conditional-independence model, a name has calm-state default probability 0.60% and stress-state weight 20.00%. If the unconditional one-year default probability is 2.40%, what stress-state default probability is implied?数理金融中等数值题未尝试面试订阅2248State-Mixture Copula Calibration 3A name's one-year default probability is modeled as a mixture of a calm state and a stress state. The stress-state probability is 25.00%, the stress-state default probability is 5.50%, and the unconditional default probability is 1.93%. What calm-state default probability is implied?数理金融中等数值题未尝试面试订阅2251Basket Dependence Recovery 1Two names have one-year default probabilities 2.00% and 3.00%. A desk prices a two-name first-to-default basket using a horizon first-to-default probability of 4.40%. What joint default probability over the horizon is implied?数理金融简单数值题未尝试免费2252Basket Dependence Recovery 2A two-name basket has first-to-default probability 3.10%. Name A has default probability 1.80%, and the desk's dependence model implies joint default probability 0.40%. What default probability for name B is implied?数理金融简单数值题未尝试免费2253Basket Dependence Recovery 3Two names have one-year default probabilities 1.20% and 2.50%. The desk's copula calibration implies joint default probability 0.30%. What first-to-default probability does that imply?数理金融简单数值题未尝试免费2296Jump Compensator Recovery 1A desk uses the simplified risk-neutral drift relation mu Q = r - lambda*kappa for a jump-diffusion. If r = 3.00%, lambda = 1.2, and mu Q = 0.60%, what jump compensator kappa is implied?数理金融简单数值题未尝试免费2297Jump Compensator Recovery 2In a simplified jump-diffusion, mu Q = r - lambda*kappa. If r = 2.50%, kappa = 1.60%, and mu Q = 0.50%, what jump intensity lambda is implied?数理金融简单数值题未尝试免费2298Jump Compensator Recovery 3A risk-neutral jump-diffusion uses mu Q = r - lambda*kappa. If r = 4.00%, lambda = 0.8, and kappa = 1.00%, what is mu Q?数理金融简单数值题未尝试免费2299Jump Compensator Recovery 4A desk writes the compensated jump-diffusion drift as mu Q = r - lambda*kappa. If mu Q = 0.60%, lambda = 1.5, and kappa = -0.40%, what risk-free rate r is consistent with that setup?数理金融简单数值题未尝试免费2300Jump Compensator Recovery 5A desk uses the simplified risk-neutral drift relation mu Q = r - lambda*kappa for a jump-diffusion. If r = 1.50%, lambda = 2, and mu Q = -0.30%, what jump compensator kappa is implied?数理金融简单数值题未尝试免费2301Poisson Jump Calibration 1In a jump-diffusion with Poisson intensity lambda, the probability of zero jumps over horizon T is exp(-lambda*T). If the no-jump probability over T = 1 years is 0.36, what lambda is implied?数理金融简单数值题未尝试免费2302Poisson Jump Calibration 2The probability of at least one jump over horizon T in a Poisson jump model is 1-exp(-lambda*T). If that probability is 0.451188 over T = 1.5 years, what lambda is implied?数理金融简单数值题未尝试免费2303Poisson Jump Calibration 3A jump-diffusion has Poisson intensity lambda = 1.1. Over what horizon T would the no-jump probability equal 0.57695?数理金融简单数值题未尝试免费2304Poisson Jump Calibration 4In a Poisson jump model, the expected number of jumps over horizon T is lambda*T. If lambda = 1.8 and T = 0.75 years, what is the expected jump count?数理金融简单数值题未尝试免费2305Poisson Jump Calibration 5A desk estimates that the expected number of jumps over the next 0.5 years is 0.6. Under a Poisson jump model with expected count lambda*T, what intensity lambda is implied?数理金融简单数值题未尝试免费