| ecld-class {ldhmm} | R Documentation |
An S4 class to represent the lambda distribution
Description
The ecld class serves as an object-oriented interface for the lambda distribution,
which is just the exponential power distribution in GSL and Wolfram.
Slots
callthe match.call slot
lambdanumeric
sigmanumeric
munumeric
Details
The lambda distribution is just the exponential power distribution in GSL and Wolfram, with a different definition in the exponent of the stretched exponential function.
The distribution is symmetric. Its PDF is
P\left(x; \lambda, \sigma, \mu\right)
\equiv\, \frac{1}{\lambda \Gamma\left(\frac{2}{\lambda}\right) \sigma}
e^{-{\left|\frac{x-\mu}{\sigma}\right|}^{\frac{2}{\lambda}}}.
where
\lambda is the shape parameter,
\sigma is the scale parameter,
\mu is the location parameter.
This functional form is not unfamiliar and has appeared under several other names, such as
generalized normal distribution and power exponential distribution, etc..
Author(s)
Stephen H. Lihn
References
This distribution is the same as gnorm and is implemented from it since V0.6.
See https://cran.r-project.org/package=gnorm.
For lambda distribution and option pricing model, see
Stephen Lihn (2015).
The Special Elliptic Option Pricing Model and Volatility Smile.
SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2707810.
Closed form solutions are derived in
Stephen Lihn (2016). Closed Form Solution and Term Structure for SPX Options.
SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2805769
and
Stephen Lihn (2017). From Volatility Smile to Risk Neutral Probability and
Closed Form Solution of Local Volatility Function.
SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2906522