In addition, the interest rate from the debt allows us to
estimate the appropriate default spread to charge on bonds.
Youcanseethepotentialinapplyingthismodeltobankloan
portfoliosto extractboth the probabilityof default and to
measurewhetheryouarecharginganinterestratethatishigh
enoughonthedebt.Infact,therearecommercialservicesthat
usefairlysophisticatedoptionpricingmodelstoestimateboth
values for firms.
ILLUSTRATION17.11:ProbabilitiesofDefaultandDefault
Spreads
WereturntoIllustration17.8andestimatetheprobabilityof
default as N(d 2 ) and the default spread, measured as the
differencebetweentheinterestrateonafirm’sdebtandthe
risk-freerate,asafunctionofthevariance.Thesevaluesare
graphedinFigure17.4.Notethattheprobabilityofdefault
climbsveryquicklyasthestandarddeviationinfirmvalue
increases, and the default spread follows it along.
FIGURE 17.4 Risk-Neutral Probability of Default and
Default Spreads