Interpretation The table shows the probability ofdefault for companies starting with aparticular credit ratingA company with an initial credit rating ofBaa has a probability of 0.181% ofdefaulting by the end of the first year,0.510% by the end of the second year,and so onRiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull20126
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Interpretation ⚫ The table shows the probability of default for companies starting with a particular credit rating ⚫ A company with an initial credit rating of Baa has a probability of 0.181% of defaulting by the end of the first year, 0.510% by the end of the second year, and so on 6
Do DefaultProbabilities Increasewith Time? For a company that starts with a goodcredit rating default probabilities tend toincrease with time For a company that starts with a poorcredit rating default probabilities tend todecrease with time7RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Do Default Probabilities Increase with Time? ⚫ For a company that starts with a good credit rating default probabilities tend to increase with time ⚫ For a company that starts with a poor credit rating default probabilities tend to decrease with time 7
Hazard Rate ys. UnconditionalDefaultProbabilityThe hazard rate or default intensity is theprobability of default over a short period oftime conditional on no earlier default The unconditional default probability is theprobability of default as seen at time zeroRiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull20128
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Hazard Rate vs. Unconditional Default Probability ⚫ The hazard rate or default intensity is the probability of default over a short period of time conditional on no earlier default ⚫ The unconditional default probability is the probability of default as seen at time zero 8
Properties ofHazard ratesSuppose that 2(t) is the hazard rate at time tThe probability of default between times t andt+△t conditional on no earlier default is 2(t)△tThe probability of default by time t is1 - e-() where ^(t) is the average hazard rate betweentime zero and time t9RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Properties of Hazard rates ⚫ Suppose that l(t) is the hazard rate at time t ⚫ The probability of default between times t and t+Dt conditional on no earlier default is l(t)Dt ⚫ The probability of default by time t is where is the average hazard rate between time zero and time t Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 9 t t e ( ) 1 −l − l(t)
RecoveryRateThe recovery rate for a bond is usuallydefined as the price of the bond 30 daysafter default as a percent of its face value10RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Recovery Rate The recovery rate for a bond is usually defined as the price of the bond 30 days after default as a percent of its face value 10