Chapter 23 Credit risk Options, Futures, and Other Derivatives, 8th Edition Copyright o John C Hull 2012
Chapter 23 Credit Risk Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 1
Credit Ratings o In the s&P rating system, AAa is the best rating. After that comes AA, A, BBB, BB, B CCC. CC, and c e The corresponding Moody' s ratings are Aaa, Aaa. baa. ba. b caa ca and c e Bonds with ratings of BBB (or Baa) and above are considered to be investment grade Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012
Credit Ratings In the S&P rating system, AAA is the best rating. After that comes AA, A, BBB, BB, B, CCC, CC, and C The corresponding Moody’s ratings are Aaa, Aa, A, Baa, Ba, B,Caa, Ca, and C Bonds with ratings of BBB (or Baa) and above are considered to be “investment grade” Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 2
Historical data Historical data provided by rating agencies are also used to estimate the probability of default Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 3
Historical Data Historical data provided by rating agencies are also used to estimate the probability of default Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 3
Cumulative Ave Default rates(%) (1970-2009, Moody's, Table 23. 1, page 522) 2345710 Aaa 00000.0120.0120.0370.1050.2450497 0.0220.0590.0910.1590.2340.3840.542 A 0.0510.1650.34105200.7171.1792046 0.17604940.91214041.92629964.851 Ba 1.1663.1865.5838.12310.39714.31819.964 4.5461042616.18821.25625.8953447344.377 Caa-C17.72329384386824609452.2865977171376 Options, Futures, and Other Derivatives, 8th Edition, Copyright o John C Hull 2012
Cumulative Ave Default Rates (%) (1970-2009, Moody’s, Table 23.1, page 522) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 4 1 2 3 4 5 7 10 Aaa 0.000 0.012 0.012 0.037 0.105 0.245 0.497 Aa 0.022 0.059 0.091 0.159 0.234 0.384 0.542 A 0.051 0.165 0.341 0.520 0.717 1.179 2.046 Baa 0.176 0.494 0.912 1.404 1.926 2.996 4.851 Ba 1.166 3.186 5.583 8.123 10.397 14.318 19.964 B 4.546 10.426 16.188 21.256 25.895 34.473 44.377 Caa-C 17.723 29.384 38.682 46.094 52.286 59.771 71.376
Interpretation o The table shows the probability of default for companies starting with a particular credit rating o a company with an initial credit rating of Baa has a probability of 0. 176% of defaulting by the end of the first year, 0.494% by the end of the second year, and So on Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 5
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 0.176% of defaulting by the end of the first year, 0.494% by the end of the second year, and so on Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 5
Do Default Probabilities Increase with Time? e 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 Options, Futures, and Other Derivatives, 8th Edition 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 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 6
Hazard rates ys Unconditional default Probabilities (page 522-523 e The hazard rate(also called default intensity) is the probability of default for a certain time period conditional on no earlier default The unconditional default probability is the probability of default for a certain time period as seen at time zero e What are the default intensities and unconditional default probabilities for a Caa rated company in the third year? Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 7
Hazard Rates vs Unconditional Default Probabilities (page 522-523) The hazard rate (also called default intensity) is the probability of default for a certain time period conditional on no earlier default The unconditional default probability is the probability of default for a certain time period as seen at time zero What are the default intensities and unconditional default probabilities for a Caa rated company in the third year? Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 7
Hazard Rate e The hazard rate that is usually quoted is an instantaneous rate e If v(t is the probability of a company surviving to time V(t+△t)-V()=-(t)(t) This leads to (1)dt The cumulative probability of default by time t is Q(0=1-e ( Options Futures, and other Derivatives, 8th Edition Copyright@ John C. Hull 2012
Hazard Rate The hazard rate that is usually quoted is an instantaneous rate If V(t) is the probability of a company surviving to time t Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 8 t t t dt Q t e t V t e V t t V t t V t t ( ) ( ) ( ) 1 ( ) ( ) ( ) ( ) ( ) 0 − − = − = + − = − The cumulative probability of default by time is This leads to
Recovery rate The recovery rate for a bond is usually defined as the price of the bond immediately after default as a percent of its face value Recovery rates tend to decrease as default rates increase Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 9
Recovery Rate Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 9 The recovery rate for a bond is usually defined as the price of the bond immediately after default as a percent of its face value Recovery rates tend to decrease as default rates increase
Recovery rates; Moody's: 1982 to 2009 Class Mean(%) 1st lien bank loan 65.6 2nd lien bank loan 32.8 Sen Unsec, bank loan 48.7 Senior Secured 49.8 Senior Unsecured 36.6 Senior Subordinated 30.7 Subordinated 313 Junior Subordinated 24.7 Options, Futures, and Other Derivatives, 8th Edition, Copyright o John C Hull 2012 10
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Recovery Rates; Moody’s: 1982 to 2009 Class Mean(%) 1st lien bank loan 65.6 2 nd lien bank loan 32.8 Sen Unsec. bank loan 48.7 Senior Secured 49.8 Senior Unsecured 36.6 Senior Subordinated 30.7 Subordinated 31.3 Junior Subordinated 24.7 10
