qsl_kurtosis_analytic: Analytic solutions on the statistics of quartic stable lambda...

In ecd: Elliptic Lambda Distribution and Option Pricing Model

Analytic solutions on the statistics of quartic stable lambda distribution

Description

Several analytic solutions on the statistics of quartic stable lambda distribution (QSLD) are implemented. These functions provide precise validation on the distribution.

Usage

qsl_kurtosis_analytic(t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0)

qsl_skewness_analytic(t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0)

qsl_variance_analytic(t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0)

qsl_std_pdf0_analytic(t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0)

qsl_pdf_integrand_analytic(
  x,
  nu,
  t = 1,
  nu0 = 0,
  theta = 1,
  convo = 1,
  beta.a = 0,
  mu = 0
)

Arguments

t	numeric, the time parameter, where the variance is t, default is 1.
nu0	numeric, the location parameter, default is 0.
theta	numeric, the scale parameter, default is 1.
convo	numeric, the convolution number, default is 1.
beta.a	numeric, the skewness parameter, default is 0. This number is annualized by sqrt(t).
x	numeric, vector of responses.
nu	numeric, vector of nu in the pdf integrand, starting from 0 (not nu0).
mu	numeric, the location parameter, default is 0.

Value

numeric

Author(s)

Stephen H-T. Lihn

References

For more detail, see Appendix C of Stephen Lihn (2017). A Theory of Asset Return and Volatility under Stable Law and Stable Lambda Distribution. SSRN: 3046732, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3046732.

Examples

  # obtain the variance for SPX 1-day distribution
  var <- qsl_variance_analytic(t=1/250, nu0=6.92/100, theta=1.17/100, convo=2, beta=-1.31)

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