The Q operator generates the normalized implied volatility \(\sigma_1(k)/\sigma\).
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).
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)
an object of ecld class with built-in \(\rho, \epsilon\)
numeric, a vector of \(\sigma\)-normalized log-strike
character, specifying option type:
c (default) or p.
numeric, delta of ki for calculating slope
numeric, a vector of log-strike
numeric, the ATM implied log-strike. It is derived from ATM volatility times sqare root of time to expiration.
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.