Chapter 24 Credit Risk,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,1,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 Moodys 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, 9th Edition, Copyright John C. Hull 2014,2,Estimating Default Probabilities,Alternatives: use historical data use credit spreads use Mertons model,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,3,Historical Data,Historical data provided by rating agencies are also used to estimate the probability of default,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,4,Cumulative Ave Default Rates (%) (1970-2012, Moodys, Table 24.1, page 545),Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,5,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 0.177% of defaulting by the end of the first year, 0.495% by the end of the second year, and so on,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,6,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, 9th Edition, Copyright John C. Hull 2014,7,Conditional vs Unconditional Default Probabilities (page 545-546),The conditional default probability 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 conditional and unconditional default probabilities for a Caa rated company in the third year?,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,8,Hazard Rate,The hazard rate (also called default density), l(t), at time t is defined so that l(t)Dt is the conditional default probability for a short period between t and t+Dt If V(t) is the probability of a company surviving to time t,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,9,Recovery Rate,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,10,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, 9th Edition, Copyright John C. Hull 2014,Recovery Rates; Moodys: 1982 to 2012,11,Using Credit Spreads (Equation 24.2, page 547),Suppose s(T) is the credit spread for maturity T Average hazard rate between time zero and time T is approximatelywhere R is the recovery rate This estimate is very accurate in most situations,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,12,Explanation,Loss rate at time t is l(t)(1R) If the credit spread is compensation for this loss rate it should approximately equal,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,13,Matching Bond Prices,For more accuracy we can work forward in time choosing hazard rates that match bond prices This is another application of the bootstrap method,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,14,The Risk-Free Rate,The risk-free rate when credit spreads and default probabilities are estimated is usually assumed to be the LIBOR/swap zero rate (or sometimes 10 bps below the LIBOR/swap rate) Asset swaps provide a direct estimates of the spread of bond yields over swap rates,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,15,Real World vs Risk-Neutral Default Probabilities,The default probabilities backed out of bond prices or credit default swap spreads are risk-neutral default probabilities The default probabilities backed out of historical data are real-world default probabilities,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,16,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,A Comparison,Calculate 7-year default intensities from the Moodys data, 1970-2012, (These are real world default probabilities) Use Merrill Lynch data to estimate average 7-year default intensities from bond prices, 1996 to 2007 (these are risk-neutral default intensities) Assume a risk-free rate equal to the 7-year swap rate minus 10 basis points,17,Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014,