H2ExtGaussian3FParam-class: Three-factor H2-extendible Gaussian calibration parameter

In hsloot/cvalr: Credit Derivative Valuation in R

Three-factor H2-extendible Gaussian calibration parameter

Description

CalibrationParam for the H2-extendible Gaussian copula with Exponential margin model for the (average) default counting process with 3 parameter. Extends H2ExCalibrationParam and related to ExtGaussian2FParam.

Usage

## S4 method for signature 'H2ExtGaussian3FParam'
initialize(
  .Object,
  composition = c(2L, 3L),
  lambda = 0.1,
  nu = c(0.2, 0.3),
  rho = NULL,
  tau = NULL
)

## S4 method for signature 'H2ExtGaussian3FParam'
simulate_dt(object, ..., n_sim = 10000L)

## S4 method for signature 'H2ExtGaussian3FParam'
expected_pcds_equation(
  object,
  times,
  discount_factors,
  recovery_rate,
  coupon,
  upfront,
  ...,
  method = c("default", "prob", "mc")
)

## S4 method for signature 'H2ExtGaussian3FParam'
show(object)

Arguments

.Object	An object: see the “Initialize Methods” section.
composition	An integerish vector with the composition.
lambda	Marginal intensity.
nu	(Internal) Outer and inner bivariate dependence parameter.
rho	Outer and inner bivariate Spearman's Rho.
tau	Outer and inner bivariate Kendall's Tau.
object	A CalibrationParam-object.
...	arguments to specify properties of the new object, to be passed to initialize().
n_sim	Number of samples.
times	A non-negative numeric vector of timepoints.
discount_factors	Non-negative numeric vector for the discount factors for the timepoints.
recovery_rate	Non-negative number between zero and one for the recovery rate..
coupon	Numeric number for the running coupon.
upfront	Numeric number for the upfront payment.
method	Calculation method (either "default", "prob" (requires implementation of probability_distribution), or "mc").

Details

The model is defined by the assumption that the multivariate default times τ = (τ_1, …, τ_d) are from a H2-extendible Gaussian copula model with Exponential margins. The model is specified by three parameters (in addition to the composition): The marginal rate lambda and the (internal) outer and inner dependency parameters nu (Pearson correlation). The dependence parameter nu should not be set by the user; instead they should provide either rho (Spearman's Rho) or tau (Kendall's Tau). The parameters rho or tau should be between zero and one, of length 2, and non-decreasing; the first value represents the outer dependence between components of different partition elements and the second value represents the inner depenence between components of the same partition element. The link between Spearman's Rho or Kendall's Tau and the internal dependence parameter (Pearson correlation) is

• ρ = 2 \sin(ρ_S \cdot π / 6) and ρ_S = 6 / π \cdot \arcsin(ρ/2)

• ρ = \sin(τ \cdot π / 2) and τ = 2 / π \cdot \arcsin(ρ)

For details on the underlying extendible model, see ExtGaussian2FParam.

Functions

• initialize(H2ExtGaussian3FParam): Constructor

• simulate_dt(H2ExtGaussian3FParam): simulates the vector of default times and returns a matrix x with dim(x) == c(n_sim, getDimension(object)).

• expected_pcds_equation(H2ExtGaussian3FParam): calculates the payoff equation for a portfolio CDS (vectorized w.r.t. the argumentes recovery_rate, coupon, and upfront).

• show(H2ExtGaussian3FParam): Display the object.

Slots

lambda

A non-negative number for the marginal rate.

nu

A numeric vector of length 2 for the model specific dependence parameters (global and component specific; range depends on specific model). Use rho or tau in the constructor to set dependence parameter.

Simulation

The default times are sampled in a two-stage procedure: First a sample is drawn from the Gaussian copula whose correlation matrix reflect the inner- and outer-dependency parameters, i.e. ρ_{i j} = ν_1 if i,j are from different elements of the partition and ρ_{i j} = ν_2 if i j are from the same element of the partition; then the results are transformed using stats::qexp().

Expected portfolio CDS loss

The expected portfolio CDS loss for recovery rate R is calculated using that

\mathbb{E}[g(L_t)] = (1 - R) \cdot F(t)

with g(x) = (1 - R) \cdot x and F being the Exponential distribution function for rate λ.

Examples

H2ExtGaussian3FParam()
H2ExtGaussian3FParam(composition = c(2L, 4L, 2L), lambda = 8e-2, rho = c(3e-1, 5e-1))
H2ExtGaussian3FParam(composition = c(2L, 4L, 2L), lambda = 8e-2, tau = c(3e-1, 5e-1))
parm <- H2ExtGaussian3FParam(composition = c(2L, 4L, 2L), lambda = 8e-2, rho = c(2e-1, 7e-1))
simulate_dt(parm, n_sim = 5L)

parm <- H2ExtGaussian3FParam(c(3, 3, 4, 5), 8e-2, rho = c(3e-1, 6e-1))
expected_pcds_equation(
  parm, times = seq(25e-2, 5, by = 25e-2), discount_factors = rep(1, 20L), recovery_rate = 0.4,
  coupon = 1e-1, upfront = 0)
expected_pcds_equation(
  parm, times = seq(25e-2, 5, by = 25e-2), discount_factors = rep(1, 20L), recovery_rate = 0.4,
  coupon = 1e-1, upfront = 0, method = "mc", n_sim = 1e1)

hsloot/cvalr documentation built on Sept. 24, 2022, 9:25 a.m.