ecld.op_Q: The Q operator in option pricing model

In ecd: Elliptic Lambda Distribution and Option Pricing Model

The Q operator in option pricing model

Description

The Q operator generates the normalized implied volatility σ_1(k)/σ. cld.op_Q_skew calculates the skew in Q space by ki and +/- dki/2. cld.op_Q_skew_by_k_lm calculates the skew in Q space by lm on a vector of k. ki is derived internally from (k-mu-rho)/sigma. ecld.fixed_point_atm_Q_left is the left hand side of fixed point ATM hypothesis. ecld.fixed_point_atm_Q_right is the right hand side of fixed point ATM hypothesis, assuming shift is stored in rho. ecld.fixed_point_atm_ki is the ATM ki in fixed point ATM hypothesis. assuming shift is stored in rho. ecld.fixed_point_shift is the utility for the standard shift algorithm, -(atm_imp_k - mu).

Usage

ecld.op_Q(object, ki, otype = "c")

ecld.op_Q_skew(object, ki, dki = 0.1, otype = "c")

ecld.op_Q_skew_by_k_lm(object, k, otype = "c")

ecld.fixed_point_atm_Q_left(object, otype = "c")

ecld.fixed_point_atm_ki(object)

ecld.fixed_point_atm_Q_right(object)

ecld.fixed_point_shift(object, atm_imp_k)

Arguments

object	an object of ecld class with built-in ρ, ε
ki	numeric, a vector of σ-normalized log-strike
otype	character, specifying option type: c (default) or p.
dki	numeric, delta of ki for calculating slope
k	numeric, a vector of log-strike
atm_imp_k	numeric, the ATM implied log-strike. It is derived from ATM volatility times sqare root of time to expiration.

Value

a numeric vector, representing Q or skew of Q. For ecld.fixed_point_atm_ki, it is ATM ki. For ecld.fixed_point_shift, it is the shift.

Author(s)

Stephen H. Lihn

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