The isk-Free ate e The risk-free rate when default probabilities are estimated is usually assumed to be the LIBOR/swap zero rate(or sometimes 10 bps below the LIBOR/swap rate) e Asset swaps provide a direct estimates of the spread of bond yields over swap rates Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 16
The Risk-Free Rate The risk-free rate when 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, 8th Edition, Copyright © John C. Hull 2012 16
Real world vs risk-Neutral default Probabilities e The default probabilities backed out of bond prices or credit default swap spreads are risk neutral default probabilities a The default probabilities backed out of historical data are real-world default probabilities Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 17
Real World vs Risk-Neutral Default Probabilities The default probabilities backed out of bond prices or credit default swap spreads are riskneutral default probabilities The default probabilities backed out of historical data are real-world default probabilities Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 17
A Comparison o Calculate 7-year default intensities from the Moodys data, 1970-2009, (These are real orld default probabilities) e Use Merrill Lynch data to estimate average 7- year default intensities from bond prices, 1996 to 2007 (these are risk-neutral default intensities) A Assume a risk-free rate equal to the 7-year swap rate minus 10 basis points Options, Futures, and Other Derivatives, 8th Edition Copyright@ John C. Hull 2012 18
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 A Comparison Calculate 7-year default intensities from the Moody’s data, 1970-2009, (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 18