ExtMOParam-class: Extendible Marshall-Olkin calibration parameter

In hsloot/cvalr: Credit Derivative Valuation in R

Extendible Marshall–Olkin calibration parameter

Description

CalibrationParam-class for the extendible Marshall-Olkin model for the average default counting process. Extends ExtMOParam.

Usage

## S4 method for signature 'ExtMOParam'
initialize(.Object, dim, bf)

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

Arguments

.Object	An object: see the “Initialize Methods” section.
dim	Dimension.
bf	Bernstein function.
object	Any R object

Details

The model is defined by the assumption that the multivariate default times τ = (τ_1, …, τ_d) are extendible Marshall-Olkin. The joint survival function of all portfolio items is

P(τ > t) = \exp{(- a_0 t_{[1]} - \cdots - a_{d-1} t_{[d]})} ,

for t_{[1]} ≥q \cdots ≥q t_{[d]} begin the descending version of t and

a_{i} = ∑_{l=0}^{d-i-1} \binom{d-i-1}{l} λ_{l+1} .

The parameter are implicitly defined by a +Bernstein function* ψ (which is provided to the constructor):

a_{i} = ψ{(i+1)} - ψ{(i)} .

Functions

• initialize(ExtMOParam): Constructor

• show(ExtMOParam): Display the object.

Slots

bf

The Bernstein function of the extendible Marshall-Olkin distribution (see rmo::BernsteinFunction).

Examples

ExtMOParam()
ExtMOParam(
  dim = 2,
  bf = rmo::ScaledBernsteinFunction(
    scale = 0.05,
    original = rmo::SumOfBernsteinFunctions(
      first = rmo::ConstantBernsteinFunction(constant = 0.4),
      second = rmo::LinearBernsteinFunction(scale = 1 - 0.4))
    ))

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