Credit: Credit Risk Modelling
In QRM: Provides R-Language Code to Examine Quantitative Risk Management Concepts
Description
Usage
Arguments
Details
See Also
Examples
Description
Functions for modelling credit risk:
Bernoulli mixture model with prescribed default and joint
default probabilities
Bernoulli mixture model with Clayton copula dependencies of
default.
Probitnormal Mixture of Bernoullis
Beta-Binomial Distribution
Logitnormal-Binomial Distribution
Probitnormal-Binomial Distribution
Usage
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cal.beta(pi1, pi2)
cal.claytonmix(pi1, pi2)
cal.probitnorm(pi1, pi2)
dclaytonmix(x, pi, theta)
pclaytonmix(q, pi, theta)
rclaytonmix(n, pi, theta)
rtcopulamix(n, pi, rho.asset, df)
dprobitnorm(x, mu, sigma)
pprobitnorm(q, mu, sigma)
rprobitnorm(n, mu, sigma)
rbinomial.mixture(n = 1000, m = 100,
model = c("probitnorm", "logitnorm", "beta"), ...)
rlogitnorm(n, mu, sigma)
fit.binomial(M, m)
fit.binomialBeta(M, m, startvals = c(2, 2), ses = FALSE, ...)
fit.binomialLogitnorm(M, m, startvals = c(-1, 0.5), ...)
fit.binomialProbitnorm(M, m, startvals = c(-1, 0.5), ...)
momest(data, trials, limit = 10)
Arguments
data
vector, numbers of defaults in each time period.
df
numeric, degree of freedom.
limit
intgeger, maximum order of joint default probability
to estimate.
M
vector, count of successes.
m
vector, count of trials.
model
character, name of mixing distribution.
mu
numeric, location parameter.
n
integer, count of random variates.
pi
numeric, default probability.
pi1
numeric, default probability.
pi2
numeric, joint default probability.
q
numeric, values at which CDF should be evaluated.
sigma
numeric, scale parameter.
ses
logical, whether standard errors should be returned.
startvals
numeric, starting values.
theta
numeric, parameter of distribution.
trials
vector, group sizes in each time period.
x
numeric, values at which density should be evaluated.
rho.asset
numeric, asset correlation parameter.
...
ellipsis, arguments are passed down to either mixing
distribution or nlminb().
Details
cal.beta(): calibrates a beta mixture distribution on unit
interval to give an exchangeable Bernoulli mixture model with
prescribed default and joint default probabilities (see pages 354-355
in QRM).
cal.claytonmix(): calibrates a mixture distribution on unit
interval to give an exchangeable Bernoulli mixture model with
prescribed default and joint default probabilities. The mixture
distribution is the one implied by a Clayton copula model of default
(see page 362 in QRM).
cal.probitnorm(): calibrates a probitnormal mixture
distribution on unit interval to give an exchangeable Bernoulli
mixture model with prescribed default and joint default probabilities
(see page 354 in QRM).
dclaytonmix(), pclaytonmix(), rclaytonmix():
density, cumulative probability, and random generation for a mixture
distribution on the unit interval which gives an exchangeable
Bernoulli mixture model equivalent to a Clayton copula model (see page
362 in QRM).
fit.binomial(): fits binomial distribution by maximum
likelihood.
dprobitnorm(), pprobitnorm(), rprobitnorm():
density, cumulative probability and random number generation for
distribution of random variable Q on unit interval such that the
probit transform of Q has a normal distribution with parameters
mu and sigma (see pages 353-354 in QRM).
fit.binomialBeta(): fit a beta-binomial distribution by maximum
likelihood.
fit.binomialLogitnorm(): fits a mixed binomial distribution
where success probability has a logitnormal distribution. Lower and
upper bounds for the input parameters M and m can be specified by
means of the arguments lower and upper, which are passed to
nlminb(). If convergence occurs at an endpoint of either limit,
one need to reset lower and upper parameter estimators and run the
function again.
fit.binomialProbitnorm(): Fits a mixed binomial distribution
where success probability has a probitnormal distribution. Lower and
upper bounds for the input parameters M and m can be specified by
means of the arguments lower and upper, which are passed to
nlminb(). If convergence occurs at an endpoint of either limit,
one need to reset lower and upper parameter estimators and run the
function again.
momest(): calculates moment estimator of default probabilities
and joint default probabilities for a homogeneous group. First
returned value is default probability estimate; second value is
estimate of joint default probability for two firms; and so on (see
pages 375-376 in QRM).
rbinomial.mixture(): random variates from mixed binomial
distribution (see pages 354-355 and pages 375-377 of QRM).
rlogitnorm(): Random number generation for distribution of
random variable Q on unit interval such that the probit transform of Q
has a normal distribution with parameters mu and
sigma (see pages 353-354 in QRM).
rtcopulamix(): random generation for mixing distribution on
unit interval yielding Student's t copula model (see page 361 in QRM,
exchangeable case of this model is considered).
See Also
Examples
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## calibrating models
pi.B <- 0.2
pi2.B <- 0.05
probitnorm.pars <- cal.probitnorm(pi.B, pi2.B)
probitnorm.pars
beta.pars <- cal.beta(pi.B, pi2.B)
beta.pars
claytonmix.pars <- cal.claytonmix(pi.B, pi2.B)
claytonmix.pars
q <- (1:1000) / 1001
q <- q[q < 0.25]
p.probitnorm <- pprobitnorm(q, probitnorm.pars[1],
probitnorm.pars[2])
p.beta <- pbeta(q, beta.pars[1], beta.pars[2])
p.claytonmix <- pclaytonmix(q, claytonmix.pars[1],
claytonmix.pars[2])
scale <- range((1 - p.probitnorm), (1 - p.beta), (1 - p.claytonmix))
plot(q, (1 - p.probitnorm), type = "l", log = "y", xlab = "q",
ylab = "P(Q > q)",ylim=scale)
lines(q, (1 - p.beta), col = 2)
lines(q, (1 - p.claytonmix), col = 3)
legend("topright", c("Probit-normal", "Beta", "Clayton-Mixture"),
lty=rep(1,3),col = (1:3))
## Clayton Mix
pi.B <- 0.0489603
pi2.B <- 0.003126529
claytonmix.pars <- cal.claytonmix(pi.B, pi2.B)
claytonmix.pars
q <- (1:1000) / 1001
q <- q[q < 0.25]
d.claytonmix <- dclaytonmix(q, claytonmix.pars[1], claytonmix.pars[2])
head(d.claytonmix)
## SP Data
data(spdata.raw)
attach(spdata.raw)
BdefaultRate <- Bdefaults / Bobligors
## Binomial Model
mod1a <- fit.binomial(Bdefaults, Bobligors)
## Binomial Logitnorm Model
mod1b <- fit.binomialLogitnorm(Bdefaults, Bobligors)
## Binomial Probitnorm Model
mod1c <- fit.binomialProbitnorm(Bdefaults, Bobligors)
## Binomial Beta Model
mod1d <- fit.binomialBeta(Bdefaults, Bobligors);
## Moment estimates for default probabilities
momest(Bdefaults, Bobligors)
pi.B <- momest(Bdefaults, Bobligors)[1]
pi2.B <- momest(Bdefaults, Bobligors)[2]
## Probitnorm
probitnorm.pars <- cal.probitnorm(pi.B, pi2.B)
q <- (1:1000)/1001
q <- q[ q < 0.25]
d.probitnorm <- dprobitnorm(q, probitnorm.pars[1], probitnorm.pars[2])
p <- c(0.90,0.95,0.975,0.99,0.995,0.999,0.9999,0.99999,0.999999)
sigma <- 0.2 * 10000 / sqrt(250)
VaR.t4 <- qst(p, df = 4, sd = sigma, scale = TRUE)
VaR.t4
detach(spdata.raw)
## Binomial Mixture Models
pi <- 0.04896
pi2 <- 0.00321
beta.pars <- cal.beta(pi, pi2)
probitnorm.pars <- cal.probitnorm(pi, pi2)
n <- 1000
m <- rep(500, n)
mod2a <- rbinomial.mixture(n, m, "beta", shape1 = beta.pars[1],
shape2 = beta.pars[2])
mod2b <- rbinomial.mixture(n, m, "probitnorm",
mu = probitnorm.pars[1],
sigma = probitnorm.pars[2])
Example output
Loading required package: gsl
Loading required package: Matrix
Loading required package: mvtnorm
Loading required package: numDeriv
Loading required package: timeSeries
Loading required package: timeDate
Attaching package: 'QRM'
The following object is masked from 'package:base':
lbeta
mu sigma rho.asset
-0.8983228 0.3732059 0.1222547
a b
3 12
pi theta
0.20000000 0.09982679
pi theta
0.04896030 0.03198761
[1] 0.001142736 0.021818856 0.103356236 0.285265923 0.592723408 1.035450932
[1] 4.896030e-02 3.126529e-03 2.485062e-04 2.320990e-05 2.386235e-06
[6] 2.576897e-07 2.836485e-08 3.122301e-09 3.395502e-10 3.619895e-11
[1] 137.1341 190.6782 248.3328 335.1372 411.8028 641.5889 1165.7670
[8] 2086.8939 3718.8363
QRM documentation built on April 14, 2020, 6:49 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details See Also Examples
Description
Functions for modelling credit risk:
Bernoulli mixture model with prescribed default and joint default probabilities
Bernoulli mixture model with Clayton copula dependencies of default.
Probitnormal Mixture of Bernoullis
Beta-Binomial Distribution
Logitnormal-Binomial Distribution
Probitnormal-Binomial Distribution
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | cal.beta(pi1, pi2)
cal.claytonmix(pi1, pi2)
cal.probitnorm(pi1, pi2)
dclaytonmix(x, pi, theta)
pclaytonmix(q, pi, theta)
rclaytonmix(n, pi, theta)
rtcopulamix(n, pi, rho.asset, df)
dprobitnorm(x, mu, sigma)
pprobitnorm(q, mu, sigma)
rprobitnorm(n, mu, sigma)
rbinomial.mixture(n = 1000, m = 100,
model = c("probitnorm", "logitnorm", "beta"), ...)
rlogitnorm(n, mu, sigma)
fit.binomial(M, m)
fit.binomialBeta(M, m, startvals = c(2, 2), ses = FALSE, ...)
fit.binomialLogitnorm(M, m, startvals = c(-1, 0.5), ...)
fit.binomialProbitnorm(M, m, startvals = c(-1, 0.5), ...)
momest(data, trials, limit = 10)
|
Arguments
data |
|
df |
|
limit |
|
M |
|
m |
|
model |
|
mu |
|
n |
|
pi |
|
pi1 |
|
pi2 |
|
q |
|
sigma |
|
ses |
|
startvals |
|
theta |
|
trials |
|
x |
|
rho.asset |
|
... |
ellipsis, arguments are passed down to either mixing
distribution or |
Details
cal.beta(): calibrates a beta mixture distribution on unit
interval to give an exchangeable Bernoulli mixture model with
prescribed default and joint default probabilities (see pages 354-355
in QRM).
cal.claytonmix(): calibrates a mixture distribution on unit
interval to give an exchangeable Bernoulli mixture model with
prescribed default and joint default probabilities. The mixture
distribution is the one implied by a Clayton copula model of default
(see page 362 in QRM).
cal.probitnorm(): calibrates a probitnormal mixture
distribution on unit interval to give an exchangeable Bernoulli
mixture model with prescribed default and joint default probabilities
(see page 354 in QRM).
dclaytonmix(), pclaytonmix(), rclaytonmix():
density, cumulative probability, and random generation for a mixture
distribution on the unit interval which gives an exchangeable
Bernoulli mixture model equivalent to a Clayton copula model (see page
362 in QRM).
fit.binomial(): fits binomial distribution by maximum
likelihood.
dprobitnorm(), pprobitnorm(), rprobitnorm():
density, cumulative probability and random number generation for
distribution of random variable Q on unit interval such that the
probit transform of Q has a normal distribution with parameters
mu and sigma (see pages 353-354 in QRM).
fit.binomialBeta(): fit a beta-binomial distribution by maximum
likelihood.
fit.binomialLogitnorm(): fits a mixed binomial distribution
where success probability has a logitnormal distribution. Lower and
upper bounds for the input parameters M and m can be specified by
means of the arguments lower and upper, which are passed to
nlminb(). If convergence occurs at an endpoint of either limit,
one need to reset lower and upper parameter estimators and run the
function again.
fit.binomialProbitnorm(): Fits a mixed binomial distribution
where success probability has a probitnormal distribution. Lower and
upper bounds for the input parameters M and m can be specified by
means of the arguments lower and upper, which are passed to
nlminb(). If convergence occurs at an endpoint of either limit,
one need to reset lower and upper parameter estimators and run the
function again.
momest(): calculates moment estimator of default probabilities
and joint default probabilities for a homogeneous group. First
returned value is default probability estimate; second value is
estimate of joint default probability for two firms; and so on (see
pages 375-376 in QRM).
rbinomial.mixture(): random variates from mixed binomial
distribution (see pages 354-355 and pages 375-377 of QRM).
rlogitnorm(): Random number generation for distribution of
random variable Q on unit interval such that the probit transform of Q
has a normal distribution with parameters mu and
sigma (see pages 353-354 in QRM).
rtcopulamix(): random generation for mixing distribution on
unit interval yielding Student's t copula model (see page 361 in QRM,
exchangeable case of this model is considered).
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | ## calibrating models
pi.B <- 0.2
pi2.B <- 0.05
probitnorm.pars <- cal.probitnorm(pi.B, pi2.B)
probitnorm.pars
beta.pars <- cal.beta(pi.B, pi2.B)
beta.pars
claytonmix.pars <- cal.claytonmix(pi.B, pi2.B)
claytonmix.pars
q <- (1:1000) / 1001
q <- q[q < 0.25]
p.probitnorm <- pprobitnorm(q, probitnorm.pars[1],
probitnorm.pars[2])
p.beta <- pbeta(q, beta.pars[1], beta.pars[2])
p.claytonmix <- pclaytonmix(q, claytonmix.pars[1],
claytonmix.pars[2])
scale <- range((1 - p.probitnorm), (1 - p.beta), (1 - p.claytonmix))
plot(q, (1 - p.probitnorm), type = "l", log = "y", xlab = "q",
ylab = "P(Q > q)",ylim=scale)
lines(q, (1 - p.beta), col = 2)
lines(q, (1 - p.claytonmix), col = 3)
legend("topright", c("Probit-normal", "Beta", "Clayton-Mixture"),
lty=rep(1,3),col = (1:3))
## Clayton Mix
pi.B <- 0.0489603
pi2.B <- 0.003126529
claytonmix.pars <- cal.claytonmix(pi.B, pi2.B)
claytonmix.pars
q <- (1:1000) / 1001
q <- q[q < 0.25]
d.claytonmix <- dclaytonmix(q, claytonmix.pars[1], claytonmix.pars[2])
head(d.claytonmix)
## SP Data
data(spdata.raw)
attach(spdata.raw)
BdefaultRate <- Bdefaults / Bobligors
## Binomial Model
mod1a <- fit.binomial(Bdefaults, Bobligors)
## Binomial Logitnorm Model
mod1b <- fit.binomialLogitnorm(Bdefaults, Bobligors)
## Binomial Probitnorm Model
mod1c <- fit.binomialProbitnorm(Bdefaults, Bobligors)
## Binomial Beta Model
mod1d <- fit.binomialBeta(Bdefaults, Bobligors);
## Moment estimates for default probabilities
momest(Bdefaults, Bobligors)
pi.B <- momest(Bdefaults, Bobligors)[1]
pi2.B <- momest(Bdefaults, Bobligors)[2]
## Probitnorm
probitnorm.pars <- cal.probitnorm(pi.B, pi2.B)
q <- (1:1000)/1001
q <- q[ q < 0.25]
d.probitnorm <- dprobitnorm(q, probitnorm.pars[1], probitnorm.pars[2])
p <- c(0.90,0.95,0.975,0.99,0.995,0.999,0.9999,0.99999,0.999999)
sigma <- 0.2 * 10000 / sqrt(250)
VaR.t4 <- qst(p, df = 4, sd = sigma, scale = TRUE)
VaR.t4
detach(spdata.raw)
## Binomial Mixture Models
pi <- 0.04896
pi2 <- 0.00321
beta.pars <- cal.beta(pi, pi2)
probitnorm.pars <- cal.probitnorm(pi, pi2)
n <- 1000
m <- rep(500, n)
mod2a <- rbinomial.mixture(n, m, "beta", shape1 = beta.pars[1],
shape2 = beta.pars[2])
mod2b <- rbinomial.mixture(n, m, "probitnorm",
mu = probitnorm.pars[1],
sigma = probitnorm.pars[2])
|
Example output
Loading required package: gsl
Loading required package: Matrix
Loading required package: mvtnorm
Loading required package: numDeriv
Loading required package: timeSeries
Loading required package: timeDate
Attaching package: 'QRM'
The following object is masked from 'package:base':
lbeta
mu sigma rho.asset
-0.8983228 0.3732059 0.1222547
a b
3 12
pi theta
0.20000000 0.09982679
pi theta
0.04896030 0.03198761
[1] 0.001142736 0.021818856 0.103356236 0.285265923 0.592723408 1.035450932
[1] 4.896030e-02 3.126529e-03 2.485062e-04 2.320990e-05 2.386235e-06
[6] 2.576897e-07 2.836485e-08 3.122301e-09 3.395502e-10 3.619895e-11
[1] 137.1341 190.6782 248.3328 335.1372 411.8028 641.5889 1165.7670
[8] 2086.8939 3718.8363
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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