ecd (version 0.9.2.4)

qsl_kurtosis_analytic: 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

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

# NOT RUN {
  # 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)
# }