ecd-class: The ecd class

In ecd: Elliptic Lambda Distribution and Option Pricing Model

The ecd class

Description

This S4 class is the major object class for elliptic lambda distribution. It stores the ecd parameters, numerical constants that facilitates quadpack integration, statistical attributes, and optionally, an internal structure for the quantile function.

Slots

call

The match.call slot

alpha,gamma,sigma,beta,mu

a length-one numeric. These are core ecd parameters.

cusp

a length-one numeric as cusp indicator. 0: not a cusp; 1: cusp specified by alpha; 2: cusp specified by gamma.

lambda

a length-one numeric, the leading exponent for the special model, default is 3.

R,theta

a length-one numeric. These are derived ecd parameters in polar coordinate.

use.mpfr

logical, internal flag indicating whether to use mpfr.

const

A length-one numeric as the integral of exp(y(x)) that normalizes the PDF.

const_left_x

A length-one numeric marking the left point of PDF integration.

const_right_x

A length-one numeric marking the right point of PDF integration.

stats

A list of statistics, see ecd.stats for more information.

quantile

An object of ecdq class, for quantile calculation.

model

A vector of four strings representing internal classification: long_name.skew, codelong_name, short_name.skew, short_name. This slot doesn't have formal use yet.

Details

The elliptic lambda distribution is the early research target of what becomes the stable lambda distribution. It is inspired from elliptic curve, and is defined by a depressed cubic polynomial,

-y(z)^3 - ≤ft(γ+β z\right) y(z) + α = z^2,

where y(z) must approach minus infinity as z approaches plus or minus infinity. The density function is defined as

P≤ft(x; α, γ, σ, β, μ\right) \equiv\, \frac{1}{C\,σ} e^{y≤ft(≤ft|\frac{x-μ}{σ}\right|\right)},

and C is the normalization constant,

C = \int_{-∞}^{∞}e^{y(z)}\,dz,

where α and γ are the shape parameters, σ is the scale parameter, β is the asymmetric parameter, μ is the location parameter.

Author(s)

Stephen H. Lihn

References

For elliptic lambda distribution, see Stephen Lihn (2015). On the Elliptic Distribution and Its Application to Leptokurtic Financial Data. SSRN: https://www.ssrn.com/abstract=2697911

ecd documentation built on May 10, 2022, 1:07 a.m.