Index
A
Abramowitz, M., 216
ABRS, 67
Accuracy ratio, 145. See also Hull-White model; Merton model; Vasicek-Kealhofer model
Actuarial science, 84
Adams, K, 34
Aggregate debt structure, 45
Agrawal, D., 163
All-orders result, 177
Altman, E., 34, 62, 75, 99, 184
Andersen, P., 99
Anderson, R., 62
Anderson and Darling Statistic, 203
Anderson-Darling criterion, 208
Andrade, G., 62
Ang, A., 216
A-rated debt, default probabilities (L-T model usage), 50
Arora, Navneet, 163
Asset liquidity, 43
Asset process, systematic risk, 145
Asset volatility, 138
estimation, 48
generation, 138
increase, 52
Asset-liability ratios, 43
Asymmetric correlation, presence, 206
Asymmetric exceedance correlations. See PDs
B
Baa-rated debt, default probabilities, 53
L-S model, usage, 51
L-T model, usage, 48
Backward substitutions, 108, 111
Bakshi, F., 130
Balance sheet data, unavailability, 8
Bangia, A., 99
Bankruptcy
costs/taxes, impact, 133
histories, 2
Base case
default probability/horizon contrast, 56
good fit, 50
table, 47
Baseline intensity. See Time-varying baseline intensity
Basle Committee on Banking Supervision, 187
Beta distribution, usefulness, 68
Bharath, S., 75
Bhatia, M., 76
Biostatistics, 84
Bivariate intensity
non-parametric estimator, 83
Black, F., 62, 76, 130, 163, 185
Black option pricing model, 54
Black-Scholes models, default occurrence, 121
Blume, M., 99
Bond value
determination, 112
random variable, 171
usage, 116
Bonds. See Coupon-paying bonds
credit quality order, Moody's rating categories, 190
data, descriptive statistics, 142–143
embedded options, exclusion, 142
markets, liquidity problems, 152
maturity date, 171
time to maturity, cumulative percentage distribution, 157
valuation, business modeling approach. See High-yield bond valuation
Book-to-market factor, 7
Book-to-market stocks, 12
Bootstrapping, 156. See also Pointwise confidence
bond availability, 157
procedure, 142
usage. See Zero-coupon yield curve
Borgan, Ø., 99
Bouye, E., 216
B-rated debt, default probabilities
L-S model, usage, 51
L-T model, usage, 49
Briys, E., 117
Brownian motion, 38
Brys, E., 62
Bubble component analysis. See Stock prices
Buckets, division, 86
Business cycles
regimes, existence, 79
Business model, usage, 103
Business modeling approach. See High-yield bond valuation
Business prospects, 43
C
Calibration. See Debt
Capital allocation decisions. See Internal capital allocation decisions
Capital asset turnover ratio, 104
Capital cost, 105. See also Firms
Capital structure, 41. See also Long-term capital structure; Rolled over capital structure; Stationary capital structure
usage, 103
Carey, M., 76
Carpenter, J., 62
Cash flows. See Debt
growth, 43
Catty, L., 99
CDS. See Credit default swap
CEDF. See Cumulative EDF
Center for Research in Security Prices (CRSP), 2
data, 7
T-bill yield, availability, 11
Çetin, U., 130
Chan-Lau, J.A., 76
Chava, S., 34
Chen, J., 216
Clayton, D.G., 216
usage, 208
Collin-Dufresne, P., 34, 63, 163
COMPUSTAT, 141
Confidence bounds, 92
Confidence intervals, 90
Constant default barrier
derivation, 45
inclusion. See Default probabilities
Copulas, 191–196. See also Clayton copula; Gaussian copulas; Gumbel copulas; Normal copula; Student's t copula; Worst fit copula
approach. See Criterion-based copula approach
empirical implications, 209–210
function. See Multivariate normal copula function
selection, 169
tail loss distributions, comparison, 210, 211
Corporate assets, fraction, 173
Corporate bonds
credit spreads, predictions, 134
Merton model, 113
optimal fraction, 178
Corporate bonds, portfolio allocation (correlated default implications)
notes, 184
Corporate bonds, recovery rates. See Publicly traded corporate bonds
Corporate rate, decomposition, 172
Corporate transactions analysis, 134
Corporate zero-coupon bonds, 166
Corporate-risk-free reference curve, 134
Correlated default processes, 186
data
Correlated defaults
complementary analysis, 195
implications. See Corporate bonds
presence, 166
Correlation
asymmetry, 195
choice, 166
levels, 194
matrix, 28, 169. See also Equity model regression
Counterparty risk, inclusion, 124
Counting process theory, 83
Coupon-paying bonds, 40
Covariates, two-dimensional sets, 84
Coverage ratios, 43
Cox process, generation, 123
Credit default swap (CDS)
contract
life, 140
premium, calculation, 140
cumulative percentage distribution (spread range), 144, 158
data
calibration, 153
choice, 136
prices, differences (histogram). See Hull-White reduced-form model; Merton model; Vasicek-Kealhofer structural model
regression. See Market CDS regression; Model CDS
spread, 140
trading frequency, 141
Credit default swap (CDS) spreads
bond spreads correlation, time series. See Market CDS
buckets, difference, 151
correlation, time series. See Market/model CDS spread correlation
cross-sectional variation, 146–152, 155, 158
determinants, 159
prediction ability, 147
summary statistics, 159
Credit derivatives market, growth, 1
Credit deterioration, 142
Credit pricing models, 133
Credit quality, decline, 190
Credit risk
analysis, types, 192
management, rating systems importance (increase), 80
measure, 102
overprediction, 154
Credit risk, reduced-form models/structural models (contrast), 132
default predictive power, 144–146
empirical methodology, 141, 142–144
Credit risk models
case study, 132
importance, 102
structure. See Reduced-form credit risk models
CreditMetrics, 71
Criterion-based copula approach, 186
data
Cross-border correlations, features, 73
Cross-sectional variation. See CDS spreads
Cross-validation statistic, 20. See also Generalized cross-validation
Crouhy, M., 216
CRSP. See Center for Research in Security Prices
Cumulative default frequencies, 53
Cumulative distribution functions, 58
determination, 46
Cumulative EDF (CEDF), 139
Cumulative normal distribution function, 137
D
Das, Sanjiv R., 65, 185, 216, 217
Data
description. See Correlated default processes; Criterion-based copula approach; Equity returns
features. See Correlated default processes; Criterion-based copula approach
problems, alleviation, 136
quality/quantity, difference, 132
thinness, 79
time-series plot, 189
Davies, D., 100
Davis, M., 217
DD. See Distance to default
de Geer, S.V., 100
Debt. See also Zero-coupon debt
borrowing/retiring, 138
cash flows, 112
lattice, 111
default probabilities, L-T model (usage). See Baa-rated debt
equity (contrast), impact. See Default intensities
holders, barrier value, 122
maturity, 45
increase, 53
package. See Hilton Hotels
principal, level, 41
specification, 44
structure. See Aggregate debt structure
valuation, 115
market capitalization, relationship, 108. See also High-yield bond valuation
value, firm value, 112
Debt, structural models
appendix, 58
default probabilities, predictions, 39
Debt-to-equity ratio. See Market
Default. See Correlated defaults
correlation, 170
instantaneous rate, 128
likelihood, increase, 27
thresholds, 169
Default barrier, 138
increase, 54
stochastic process, 125
Default boundaries, 44. See also Endogenous default; Exogenous default
decrease, 46
Default costs, 44
Default data, non-parametric analysis
notes, 99
one-dimensional hazards, 88–90
transitions, move/duration dependence, 91–94
Default frequencies. See Shorter-term default frequencies
matching. See L-T model
Default implications, correlation. See Corporate bonds
Default intensities
comparison, debt/equity contrast (impact), 30–32
equivalence tests, debt prices/equity prices (usage), 31
process, analytic tractability, 5
standard error average, 22
time series graph, 22
Default losses, prediction, 42
Default parameters
estimation, 8
time series properties, analysis, 22–26
Default predictive power. See Credit risk
Default probabilities (DPs), 170, 176
behavior. See Risk-neutral default probabilities
constant default barrier, inclusion, 46
difference, 67
estimation. See Equity prices
horizon, contrast. See Base case
Kendall's τ, 191
L-S model, usage. See Baa-rated debt; B-rated debt
L-T model, usage. See A-rated debt; Baa-rated debt; B-rated debt; Single-B-rated debt
plotting, 47
predictions, 43. See also Debt
time series, 190
underprediction, 57
Default process. See Joint default process
Default protection contract, purchase, 73–74
Default rates, recovery rates (negative relationship), 67
Default risk, 166
implications, 171
literature, survey
measure transformations, 73–75
recovery conventions, 69
speculation, 75
relationship. See Structural models
Default swap. See Fair-value default swap total expected premium, 72
Default time, transformation, 126
Defaultable debt, supply, 67
Default-free bond, risk-free value, 141
Default-free interest rate, 44–45
Default-free zero-coupon bonds, 3
Default-risk measures, 145
Default-risk-free rate, 134
Dependence. See Tail dependence
empirical features. See Joint distribution
relationship, 196
DET indication, 37
Deventer, D., 117
Diebold, F., 99
Dimson, E., 34
Discount bond prices, 9
Discrete-time model, consideration, 71
Distance to default (DD)
calculation, 55
DD-to-EDF empirical mapping step, 138
empirical distribution, 133
term structure, calculation, 138
Doob-Meyer decomposition, 127
Dowd, K., 217
DPs. See Default probabilities
Duan, J.D., 130
Duffie, D., 34, 76, 130, 185, 217
Duffie-Lando model, 126
Duration
dependence. See Default data; Rating transition data
effects, 90
Dynkin, L., 185
E
Earnings per share (EPS), matching. See L-S model
Eastman Kodak Company, intensity function (time series estimates), 22
EBIT, 43
Economy-wide default risk, increase, 196
EDF. See Expected default frequency
Eigenvalues, 170
EIS. See Expected default frequency
EJV (Reuters), 141
EMBI. See Emerging Market Bond Index
Embrechts, P., 217
Emerging Market Bond Index (EMBI) (J.P. Morgan), 75
Empirical default frequencies, matching. See L-T model
Empirical EPS, matching. See L-S model
Endogenous default, 39
contrast. See Exogenous default
Epanechnikov kernel functions, usage, 85
Equity issuance, consideration, 4
Equity model regression
independent variables, correlation matrix, 28
parameter estimatics, averages, 15–19
Equity prices, bubbles, 27
existence, 2
Equity prices, default probabilities (estimation), 1
firms, involvement, 8
model performance, summary statistics, 23–25
Equity returns
computation, data description, 7–9
models, 14
time-series model, 6
Equity risk
parameters, time series properties (analysis), 22–25
premium, 29
Equity value, 137
Equivalence tests, debt prices/equity prices (usage). See Default intensities
Estimation
parameters. See Regime-switching model
phase. See Joint default process
results. See Regime-switching model
European call option, 121
Event downgrade, 87
premium, 167
Exceedance correlation plot, 206
Exceedance plot, 196
Exogenous default, 39
boundaries, L-S model, 45
endogenous default, contrast, 40
Expected default frequency (EDF), 55, 133
EDF-implied spreads (EIS), 140
Expected utility, differentiation, 74
Exposure matrix, graphical illustration, 86
External intensity estimator, 84
F
Face value, receiving, 103
Fair-value default swap, 72
Fama, E., 34
Fama-French benchmark portfolios, 7
Fama-French four-factor model, analysis, 26
Fan, J., 99
Fan, R., 216
Fanjul, G., 75
FCFs. See Free cash flows
Filtration
expansion, 126
generation, 123
reduction, 127
stopping time, 126
Finger, C., 76
Firms. See Primitive firm
capital cost, 106
debt, payoff, 123
fixed costs, 110
operating leverage, 116
perpetual debt, 115
value. See High-yield bond valuation lattice, determination, 108
volatility, 48
First-order condition, derivation, 214
First-passage time cumulative probability function, 46
Fischer, E., 63
Fixed cost, present value, 108
Fong, G., 185
Forward rates, 71
curves, estimation, 9
Four-factor asset-pricing model, 12
Fourth-degree polynomial, 9
Fractional default loss, 173
Fractional loss
fluctuations, 174
probability, 177
Free cash flows (FCFs), 107
Freed, L., 216
Frees, E.W., 217
French, K., 34
Friedman, M., 163
Frye, J., 76
Fusaro, R., 100
G
Galai, D., 216
Gaussian copulas, 207
Generalized cross-validation (GCV) statistics, 29–30
Genest, C., 217
Gersbach, H., 217
Gijbels, I., 99
Gill, R., 99
Girsanov's theorem, usage, 38
Goldberg, L., 163
Goodness of fit. See Marginal distribution
measure, 30
Gordy, M., 76
Gross return on investment (GRI), 104–108
binomial process, 106
decrease, 114
lattice
generation, 109
usage. See High-yield bond valuation
Guillen, M., 100
Gumbel, E.J., 217
Gupton, G., 76
H
Hamilton, D., 100
Hazard rates
annualization, 181
correlations, 194
graphical illustration, 205
independence, 176
joint dynamic system, 188
model, 125. See also Intensity-based hazard-rate model
application, 119
samples, 204
Heath, D., 34
Heinkel, R., 63
High-grade debt, issuance, 196
High-low regime cutoff, 200
High-yield bond valuation
approach, 102
business modeling approach, 101
notes, 117
references, 117
model
implications, 115
numerical illustration, 108–113
debt valuation, market capitalization (relationship), 111–112
High-yield companies, 107
Hilton Hotels
debt package, 112
debt structure, 111
example, 109
factors, 13
Horizon interval, 20
Hu, W., 76
Huang, M., 35
HUÍ, C.H., 130
Hull-White model (HW model), 132, 137, 140–141
accuracy ratio, 145
negative bias, 155
Hull-White reduced-form model, market/model CDS price differences (histogram), 148
HW model. See Hull-White model
Hyman, J., 185
I
Idiosyncratic risk, 196
Implied default probability density, 143
Independent variables, correlation matrix. See Equity model regression
Information sets
generation, 123
knowledge assumption, reduced-set models, 119
Information-based perspective. See Structural models
Ingersoll, J., 185
In-sample root mean squared error goodness-of-fit tests, 2
Intensities. See Downgrade intensities; Multiplicative intensities; Upgrade intensities
analysis. See Default intensities
estimator. See Bivariate intensity
estimator; Local constant
two-dimensional intensity estimator; Local linear two-dimensional intensity estimator
graphs, 82
issuer-level stochastic process, marginal distribution, 197
joint dynamic system, 188
mean estimation, stochastic process (results), 199
processes
constants, 124
mean, 199
residuals, fit (estimation results), 204
two-dimensional estimation. See Transition intensities
Intensity-based hazard-rate model, 127
Interest, spot rate, 5
Interest rates. See Default-free interest rate
constancy, 121
risk, 156
Internal capital allocation decisions, 77
Investment time horizon, 166
Issuers, cumulative percentage distribution, 143, 157
J
Jäckel, P., 185
Jarrow, Robert, 1, 34, 35, 63, 76, 118, 130, 163, 164, 217, 218
Joint default probabilities, 174
Joint default process
calibration, 204
estimation phase, 197
Joint dependence
Joint distribution, dependence (empirical features), 194–196
Joint probability distribution. See Returns
Joint stochastic process, estimation problem, 192
Jokivuolle, E., 76
Jones, E., 131
Jones, M.C., 100
Jorion, P., 185
Jump model, usage. See Rating class
Jump size, uniform distribution, 198
Jump-diffusion model
Junior debt, 103
K
Kao, D., 99
Kapadia, N., 216
Kaplan, S., 62
Kavvathas, D., 100
Kealhofer, S., 164
Keiding, N., 99
Kernel smoothing, example, 85–86
Kijima, M., 218
Kim, J., 164
Kluppelberg, C., 217
KMV approach
relationship. See L-S model; L-T model steps. See Moody's-KMV approach
KMV default boundary, 54
KMV DP, decrease, 56
Kolmogorov criterion, 209, 211
Kolmogorov distance, 203
Konstantinovsky, V., 185
Kronimus, A., 99
Kurtosis
distributions, 189
injection, 197
Kusuoka, S., 131
L
L1 distance, 201
L2 distance, 203
Lando, David, 63, 77, 130, 131, 163, 217
Lebesgue measure, 125
Lee, A.J., 218
LGD. See Loss given default
LIBOR swap rate, 167
Lim, F., 99
Linear regression, multicollinearity, 25
Linton, O., 100
Lipponer A., 217
Liquidating dividend, present value, 5–6
Liquidating payoff, 4
Liquidation value, risk premium, 38
Liquidity
spread, 114
Lo, C.F., 130
Local constant two-dimensional intensity estimator, 80
Local linear two-dimensional intensity estimator, 80
Löffler, G., 100
Log-likelihood function, 202
Longin, F., 218
Longstaff, F., 63, 117, 130, 164, 185, 218
Long-term capital structure, 41
Long-term growth rate, 110
Lonski, J., 100
Loss given default (LGD), 44, 65, 139. See also Sector-specific LGD; Seniority-specific LGD
Low-grade bonds, 166
Low-maturity bonds, 153
L-S model. See Exogenous default
empirical EPS, matching, 50–54
KMV approach, relationship, 55–56
usage. See Baa-rated debt; B-rated debt
L-T model. See Endogenous default
empirical default frequencies, matching, 47–50
KMV approach, relationship, 55–56
usage. See A-rated debt; Baa-rated debt; B-rated debt; Single-B-rated debt
Lyden, S., 164
M
MacKinlay, A., 99
Madan, D., 35, 62, 76, 130, 131, 218
Marginal distribution
choices, 209
estimation, 202
selection, 203
Marginal downgrade intensity, 89, 92, 93
Marginal effect, explanation, 88
Marginal hazard functions, non-parametric estimators (usage), 79
Marginal integration. See Default data; Rating transition data
impact, 79
Marginally integrated intensities, 97
Marginally integrated upgrade/downgrade intensities, 89, 91, 96
Mark, R., 216
Market
capitalization, 113
relationship. See Debt
value, 112
debt-to-equity ratio, 115
index
coefficient, 28
probability, 105
risk premium, 134
Sharpe ratio, 139
value. See Recovery of market value
volatility, constancy, 12
Market CDS regression, 151, 152
Market CDS spreads
bond spreads correlation, time series, 153
correlation, time series, 150
cross-sectional variation, explanation, 155
Market portfolio, return, 12
Market-microstructure noise, elimination, 8
Market/model CDS price differences, histogram, 148, 149. See also Hull-White reduced-form model; Merton model; Vasicek-Kealhofer structural model
Market/model CDS spread correlation, time series, 151
Markov assumptions, deviation, 80–81
Martin, J., 34
Martingale measure, 123
Martingale process, 105
Mauer, D., 64
Maximum likelihood estimation (MLE), 198
McLeodUSA, stock value/bond value (contrast), 113–114
McNeil, A., 217
Mean estimation, jump model usage. See Rating class
Mean process estimation. See Regime-switching environment
Mean reversion rate, 200
Measure transformations. See Default risk; Recovery; Recovery risk
Mella-Barral, P., 63
Merton, R.C., 63, 76, 131, 164, 185, 218
accuracy ratio, 145
comparison, 115
default occurrence, 121
market/model CDS price differences, histogram, 150
Mikosch, T., 217
Miller and Modigliani model (MM model), 104–105
Miller model, 104
Mithal, S., 164
MKMV. See Moody's-KMV
MLE. See Maximum likelihood estimation
MM model. See Miller and Modigliani model
Model CDS, regression, 151, 152
Model-derived value, 113
Moment expansion. See Optimal portfolio
convergence, 178
default/convergence probability, 181
Monetary value component, 4
Monte Carlo experiment, illustration, 205–206
Monte Carlo simulation, 200
usage, 197
Moody's Investors Services, 63
cycle, rating through, 81
default database, usage, 187
rating categories. See Bonds
Risk Management Services, 210
Moody's Special Report, 35
Moody's-KMV (MKMV) approach, 133
Morton, A., 34
Move dependence. See Default data; Rating transition data
Multiplicative intensities, 94–98
structure, 97
Multiplicative model
equation, 95
Multiplicative structure, additive structure (preference), 95
Multivariate normal copula function, 168–169
N
n-dimensional random vector, simulation procedure, 193
Negative net worth, 40
Neis, E., 164
Nelsen, R.B., 218
Nickell, P., 100
Noise process, addition, 125–126
Noncredit risk component, 152
Non-default-related risk, 167
Non-linear optimization procedure, 109
Non-Markovian behavior, 78
existence, 80
Non-parametric analysis. See Default data; Rating transition data
Non-parametric estimators, usage. See Marginal hazard functions
Non-parametric techniques, usage, 78, 81
Nonzero recovery, 181
fractions, inclusion. See Portfolios
Normal copula, 192
N-period default swap premium, 72
Null hypothesis, testing, 31–32
n-variate distribution, modeling, 191
O
Occurrence exposures
stratification, 91
Occurrence matrix, simulation, 90
Occurrence/exposure ratio, usage, 84
Off-diagonal elements, 171
Off-the-run securities, 152
Ogden, J., 164
One-dimensional hazards. See Default data; Rating transition data
On-the-run securities, liquidity, 152
Operating leverage. See Firms
Optimal portfolio
moment expansion, 179, 180, 182
recovery, 182
Option price process, 103
Out-of-sample forecasts, 74–75
Out-of-sample generalized cross-validation statistics, 2
Out-of-sample model fit, 30
Oversmoothing, signs, 85
P
Parameters. See Base case
estimates. See Risk premium
estimatics, averages. See Equity model regression
estimation. See Market index; Spot rate process parameter estimation
rolling estimation, 10
values set, 51
Park, B.U., 100
Payout rate, 44
PD. See Probability of default
P/E. See Price-to-earnings ratio
Pedersen, K., 34
Perpetual debt. See Firms valuation formula, 108, 116
Peura, S., 76
Pointwise confidence
interval, 90
bootstrapping, 91
sets. See Univariate intensities
Portfolios
allocation
correlated default implications. See Corporate bonds
dependence, 179
default loss probability distribution, 178
variance/skewness, 182
moment expansion. See Optimal portfolio
problems, 171–176. See also Corporate bonds
samples
nonzero recovery fractions, inclusion, 181–182
zero recovery fractions, inclusion, 176–181
volatility, 180
Power-curve testing, 136
Predictive power, comparison, 145
Price earnings ratio, proxy, 12
Price staleness, 141
Price-to-earnings ratio (P/E), analysis, 26–27
Primitive firm, 101, 104. See also High-yield bond valuation
lattice, 104
determination, 109
value, 116
Probability of default (PD)
asymmetric exceedance correlations, 195. See also Simulated PDs
averages, simulated series, 205
levels, measure, 191
time series, 189
time series, summary, 191
Protection buyer, 140
Publicly traded corporate bonds, recovery rates, 66
R
Radom-Nikodym derivative, 74
Ramaswamy, K., 164
Ramlau-Hansen, H., 100
Ramlau-Hansen estimator, 84
Rating class
downward transitions, 78
mean estimation, jump model (usage), 197–200
stochastic process, 207
Rating drift, 80
analysis, 92
Rating systems, importance (increase). See Credit risk management
Rating transition data, nonparametric analysis
notes, 99
one-dimensional hazards, 88–90
transitions, move/duration dependence, 91–94
Ratings displays, evolution, 78
Raw occurrence exposure ratios, computation, 84
Raw occurrence matrix, graphical illustration, 87
Rebonato, R., 185
Recovery. See Reduced-form models; Structural models
conventions. See Default risk; Recovery risk
equations, 70
expectation, 70
fractions, 166
disappearance, 175
zero value, assumption, 176
ratios, 43
statistics, 66
Recovery of market value (RMV), 69
Recovery of par (RP), 69
Recovery of Treasury (RT), 69
Recovery rates. See Publicly traded corporate bonds; Target recovery rate
constants, 124
decrease, 53
dependence, 68
expression, 69
maximum, 73
measure transformations, 73–75
need, 32
regime effects, impact, 68
volatility, 67
Recovery risk, literature survey
conventions, 69
measure transformations, 73–75
speculation, 75
Reduced-form credit risk models
equivalence, 7
estimation, 3
Reduced-form framework, testing, 153
Reduced-form information set, 124
Reduced-form model-implied CDS spreads, 147
Reduced-form modeling frameworks, 136
contrast, information-based perspective. See Structural models
empirical testing, 136
knowledge assumption. See Information sets
market/model CDS price differences, histogram. See Hull-White reduced-form model
origination, 118
preference, 128
structural models, contrast. See Credit risk
Reference obligation, expected recovery rate, 140
Regime determination, 200
Regime effects, impact. See Recovery rates
Regime-shifting models, metric q values, 207, 208
Regime-switching environment, mean process estimation, 200–201
Regime-switching model, 189
estimation parameters, 201
estimation results, 201
Residuals, normalization, 201
Returns, joint probability distribution, 166
Reversal aversion effect, 94
Riboulet, G., 216
Risk
level, decrease, 180
driver, volatility, 105
management, purpose, 73
Risk (magazine), 35
Risk premium. See Excess risk premium; Liquidation value; Market
parameter estimates, 25
requirement, 73
Risk-free rate, 116
excess return, source, 165
Risk-free zero curve, 142
Risk-neutral cumulative default probability, 139
Risk-neutral default probabilities, 146
behavior, 145
Risk-neutral probability, 106, 107
Rivest, L., 217
RMSE. See Root mean squared statistic
RMV. See Recovery of market value
Rogers, L.C.G., 131
Rolled over capital structure, 54
Rolling estimation procedure, 14
Root mean squared statistic (RMSE), magnitudes, 29–30
Rosenfeld, E., 131
RP. See Recovery of par
R-squared
statistic, reliability, 159
time series distribution quartiles, 155, 158
RT. See Recovery of Treasury
S
Saà-Requejo, J., 63, 76, 117, 131
Santa-Clara, P., 63, 76, 117, 131
Saraniti, D., 164
Schaefer, S., 63
Schagen, C., 99
Scheike, T., 100
Scholes/Merton option pricing model, 54
Schonbucher, P., 218
Schubert, D., 218
Schuermann, T., 99
Schwartz, E.M., 117
Schwartz, R., 35
Sector volatility, 112
Sector-specific LGD, 139
Seniority, importance, 68
Seniority-specific LGD, 139
Sharpe ratio. See Market
Shorter-term default frequencies, 39
Short-term liabilities, 54
Shumway, T., 35
Simulated PDs, asymmetric exceedance correlations, 206
Simulation models
Single-B-rated debt, default probabilities (L-T model usage), 48
Singleton, K., 34, 76, 130, 163, 185, 217
Skewed double exponential distribution, 202, 207–208, 212–214
Skewed double exponential model, 213
Sklar, A., 218
Skadeberg, T., 100
Small firm factor, 7
factors, 13
Smith, K., 35
Smoothed downgrade intensity, 88
Smoothed downgrade matrix, 88
Smoothed exposure matrix, 88
Smoothed two-dimensional intensity estimator, computation, 85
Smoothing
procedure, definition, 85
quantiles, impact, 82
techniques, usefulness, 79
Sobehart, J., 100
Solnik, B., 218
Solvency requirements, 77
Spot rate process parameter estimation, 9–11
Spreads
determinant, 158
underprediction, 134
writing, 66
Srinivasan, A., 75
SSEs. See Sums of squared errors
State variables, 126
process parameters, estimation, 9–12
Stationary capital structure, 45
Statistical probability measure, 120
Stegun, I.A., 216
Stochastic process, 120, 123. See also Default barrier
Stock prices
bubble component
existence, 4
data, unavailability, 8
Stock volatility, 113
Stohs, M., 64
inaccessibility, 123
Straumann, D., 217
Strebulaev, I., 63
Strike price, 121
Structural modeling frameworks, 136
contrast. See Credit risk
default probabilities predictions. See Debt
default risk, relationship, 43–44
reduced-form models (contrast), information-based perspective
mathematical overview, 125–128
setup, 120
usefulness, 134
Student's t copula, 192
Student's t distribution, 202
Sums of squared errors (SSEs), calculation, 96–98
Sundaram, R., 216
Swap yield curve, 167
Synthetic credit instruments, 145
Systematic risk, 196
measures, 194
Tail loss distribution, 210. See also Copulas
Tanggaard, C., 100
Target recovery rate, 52
Tauren, M., 131
Term structure, estimation, 138
Terminal value, 107
Terminal wealth values, 74
THR. See Total hazard rate
Time horizons, 47, 110. See also Investment time horizon
increase, 181
Time series distribution quartiles. See R-squared
Time series estimates, summarization, 14–15
Time series properties, analysis. See Default parameters; Equity risk
Time-dependent sample variance/correlation coefficients, 11
Time-series model. See Equity returns
Time-varying baseline intensity, 80
Total expected discounted payoffs, 72
Total expected premium. See Default swap
Total hazard rate (THR), 195–196
Trade Reporting and Compliance Engine (TRACE), 136
Transition intensities, two-dimensional estimation, 83–88
Transitions
exact dates, 82
move/duration dependence. See Default data; Rating transition data
Treasury coupon bond prices, 140
Trigger default function, 103
Tsang, S.W., 130
t-scores, averages. See Equity model regression
t-statistics, 14
Tufano, P., 216
Turnbull, S., 63, 130, 164, 217
Turner, C., 163
Two-dimensional estimation. See Transition intensities
Two-dimensional intensities
estimator, 88
computation. See Smoothed two-dimensional intensity estimator
Two-stage Monte Carlo model, 205–206
Type I error, 144
Type II error, 144
U
Uhrig-Homburg, M., 64
UMD, 7
factors, 13
Unit root rejections, summary, 25
Unit root test performance, results, 25
Univariate intensities
estimators, 83
pointwise confidence sets, 83
Unrestricted two-dimensional estimator, 95
Uppal, R., 217
U.S. Treasury prices, usage, 7
U.S. Treasury securities, coupons, 9
Utility function, change, 180
V
Valdez, E.A., 217
van Deventer, D., 34, 35, 130, 131
VAR analysis, 168
Varotto, S., 100
Vasicek-Kealhofer model (VK model), 132, 137, 138–140
accuracy ratio, 145
implementation, 139
MKMV implementation, 134
negative bias, 155
performance ability, 154
Vasicek-Kealhofer structural model, market/model CDS price differences (histogram), 149
Violet, L., 217
VK model. See Vasicek-Kealhofer model
Vogelius, M., 100
Volatility. See Portfolios; Risk
constancy. See Market. See Asset volatility
W
Wahba, G., 35
Wand, M.P., 100
Wang, S.S., 218
Wang, X., 130
Warga, A., 35
Wealth, utility (expansion), 175
Whitcomb, D., 35
Wiener process, 107
Worst fit copula, 211
X
Xiao, J., 218
Y
Yield curve, flatness (assumption), 108
Yield spreads, prediction, 42
Yildirim, Yildiray, 1, 35, 130
Z
Zechner, J., 63
Zeng, Y., 131
Zero recovery fractions, inclusion. See Portfolios
Zero-coupon bond, 55
dollar payment, 120
maturity, 121
spread, 139
Zero-coupon corporate bonds, 172
Zero-coupon debt, 40
Zero-coupon yield curve, bootstrapping(usage), 143, 157
Zhu, Fanlin, 132
Zmijewski, M.E., 35