Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 24: Credit Risk Multiple Choice Test ank: !uestions "ith #ns"ers 1. Suppose that the cumulative probability probability of a company company defaulting defaulting by years one, two, three three and four are are 3%, 6.5%, 10%, and 1.5%, respectively. respectively. !hat is the probability of default in the fourth year conditional on no earlier default" #. .5% $. 5.0% . 5.5% &. 6.0% #nswer' $ (he unconditional unconditional )& for the fourth year year is 1.5% minus minus 10% or .5%. .5%. (he probability probability of no earlier default default is *0%. (he (he )& conditional conditional on no earlier default is therefore 0.05+0.*0.05 or 5% -. !hich of the following following is usually usually used used to dene the recovery recovery rate of of a bond" #. (he value of of the bond immediately after after default as a percent percent of its face value $. (he value of of the bond immediately after after default as a percent percent of the the sum of the bond/s face value and accrued interest . (he amount nally realied realied by a bondholder bondholder as a percent of of face value value &. (he amount nally nally realied by a bondholder bondholder as a percent percent of the sum sum of the bond/s face value and accrued interest #nswer' # (he recovery recovery rate for a bond bond is usually usually dened as the value of the bond bond immediately after a default as a percent of its face value. (his is in spite of the fact that the bond holder/s claim in the event of a default in many urisdictions urisdictions is the face face value plus accrued accrued interest. interest. 3. !hich !hich of the following following is true" true" #. 2is neutral neutral default probabilities probabilities are are usually much lower than real real world default probabilities $. 2is neutral neutral default probabilities probabilities are are usually much higher than real real world default probabilities . 2is neutral neutral and real real world probabilities probabilities must be close to each other other if there are to be no arbitrage opportunities &. 2is4neutral default probabilities probabilities cannot be calculated from &S &S spreads #nswer' $ 2is neutral default probabilities are usually greater than real world default probabilities.
. # haard rate is 1% per annum. !hat is the probability of a default during the rst two years" #. -.00% $. -.0-% . 1.*% &. 1.*6% #nswer' (he probability of no default is e 0.017- 0.*0-. (he probability of default is one minus this or 0.01* 8i.e., 1.*%9. 5. !hich of the following is true #. (he default probability per year for a company always increases as we loo further ahead $. (he default probability per year for a company always decreases as we loo further ahead . Sometimes # is true and sometimes $ is true &. (he default probability per year is roughly constant for most companies #nswer' :or investment grade companies the probability of default tends to increase with time. :or non4investment grade companies the reverse is often true. 6. !hich of the following is true #. onditional default probabilities are at least as high as unconditional default probabilities $. onditional default probabilities are at least as low as unconditional default probabilities . onditional default probabilities are sometimes lower and sometimes higher than unconditional default probabilities. &. (here is no di;erence between conditional and unconditional default probabilities because a company can only default once. #nswer' # (he conditional default probability for a future time period is the unconditional default probability divided by the probability of no earlier default. (he latter is less than or ef a company/s ve year credit spread is -00 basis points and the recovery rate in the event of a default is estimated to be -0% what is the average haard rate per year over the ve years #. 0.% $. 1.-%
. 1.% &. -.5% #nswer' & (he average haard rate is the credit spread divided by one minus the recovery rate. >n this case we get 0.0-+0.0.0-5 or -.5% . !hich of the following is true #. 2ecovery rates are lower for investment grade companies $. 2ecovery rates are higher for non4investment grade companies . 2ecovery rates are negatively correlated with default rates &. 2ecovery rates are positively correlated with default rates #nswer' !hen default rates are high in the economy, recovery rates tends to be low *. !hich of the following is true #. (he asset swap spread is a measure of e?cess of the bond yield over the @>S rate $. (he asset swap spread is a measure of e?cess of the bond yield over the A>$@2+swap rate . #n asset swap e?changes the actual return on the asset for A>$@2 plus a spread &. Bone of the above #nswer' $ (he asset swap spread is a measure of the e?cess of the bond yield over A>$@2. >n an asset swap the promised cash Cows 8not the actual cash Cows9 on a bond are e?changed for A>$@2 plus a spread 10.(o be investment grade, a company has to have a credit rating of #. ## or better $. # or better . $$$ or better &. $$ or better #nswer' ompanies with credit ratings of $$$ or better are investment grade. 11.>n the Daussian copula model which of the following is true #. (he time to default for a company is assumed to be normally distributed. $. (he time to default for a company is assumed to be lognormally distributed
. (he time to default for a company is transformed to a normal distribution &. (he time to default for a company is transformed to a lognormal distribution #nswer' (he time to default for each company is transformed to a normal distribution on a percentile to percentile basis and the normal distributions are assumed to be multivariate normal. 1-.!hich of the following is true #. Betting always leads to a reduction in a company/s e?posure to a counterparty $. Betting always leads to a company/s e?posure to a counterparty either staying the same or going down . Betting always increases a company/s e?posure to a counterparty &. Betting can increase or reduce the e?posure #nswer' $ Betting means that the derivatives portfolio with a counterparty is considered to be a single transaction in the event of a default. (his cannot increase the e?posure. >f there are transactions in the portfolio with both positive and negative values the e?posure will go down. 13.!hich of the following is true #. &owngrade triggers are particularly valuable if they are widely used by a company/s counterparties $. &owngrade triggers become less valuable if they are widely used by a company/s counterparties . &owngrade triggers are useless because their impact is always anticipated by the maret &. &owngrade triggers are a two4edged sword. >f company # has a downgrade trigger for company $ then company $ has a downgrade trigger for company # #nswer' $ &owngrade triggers become less valuable if many of a company/s counterparties are using them 8as was the case with Enron and #>D9. (his is because the counterparties will re
#nswer' # >n Ferton/s model the maret value of the en Ferton/s model, the strie price is the face value of the debt 16.!hich of the following is true #. (he Daussian copula model assumes that the defaults of di;erent companies are independent. $. (he Daussian copula model assumes that defaults, conditional on the value of a factor , are independent. . (he Daussian copula model assumes that the number of defaults is normally distributed. &. Bone of the above. #nswer' $ (he Daussian copula model is analyed by noting that defaults conditional on a factor are independent 1=.# derivatives dealer has a single transaction with a company which is a long position in a ve4year option. (he $lac4Scholes4Ferton value of the option is G6. Suppose that the credit spread on ve4year bonds issued by the company is 100 basis points. !hat is the dealer/s H# per option purchased from the counterparty" #. G0.1* $. G1.1* . G0.-* &. G1.-* #nswer' (he value of the option when the counterparty/s credit ris is taen into account is 6e 0.01755.=1 and so the H# is 65.=1 or G0.-* per option purchased 1.!hich of the following is true #. # derivative dealer/s H# is the counterparty/s &H# and vice versa $. ollateral posted by the counterparty reduces H# . ollateral posted by the dealer reduces &H#
&. #ll of the above #nswer' & #, $, and are all true 1*.
(he credit spreads for a counterparty for 5 and 6 years are -% and -.-% respectively. (he recovery rate is 60%. !hat is closest to the unconditional default probability for the si?th year" #. 0.0 $. 0.05 . 0.06 &. 0.0= #nswer' (he average haard rate for the rst ve years is 0.0-+8140.690.05 or 5%. (he average haard rate for the rst si? years is 0.0--+8140.690.055 or 5.5%. (he probability of no default during the rst ve years is therefore e 40.05750.==. (he probability of no default during the rst si? years is e40.05576 0.=1*. (he probability of default during the si?th year is therefore 0.==0.=1* or appro?imately 0.06.
-0.!hich of the following is true of reditmetrics when it is used to calculate credit Ha2 #. reditmetrics taes defaults but not downgrades into account $. reditmetrics taes downgrades but not defaults into account . reditmetrics considers neither defaults nor downgrades &. reditmetrics considers both defaults and downgrades #nswer' & $y woring from the credit transition matri? reditmetrics taes both downgrades and defaults into account.
