ecop.find_fixed_point_lambda_by_atm_skew: Utility to find the fixed point lambda that matches ATM skew

Description

This utility finds the fixed point lambda from larger lambda to smaller lambda until the calculated ATM skew is smaller than ATM skew from data. It uses ecop.find_fixed_point_sd_by_lambda to locate stdev. Other smile related parameters are abstracted away via the closure function fn_get_ld1. This utility is used primarily to solve the fixed point ATM hypothesis (for VIX option smile). Note that this utility alone is not the full solution. Another utility is needed to match the two tails (via mu and epsilon). This utility doesn't handle beta either.

Usage

ecop.find_fixed_point_lambda_by_atm_skew(
  fn_get_ld1,
  lambda,
  step,
  atm_skew,
  k_atm,
  ttm,
  otype = "c",
  verbose = TRUE,
  msg_prefix = "",
  min_lambda = 1.1
)

Arguments

fn_get_ld1

function, takes stdev, lambda, beta as input, return ld1 object via ecop.get_ld_triple. This closure function encapulates mu_plus_ratio, epsilon_ratio, atm_imp_k.

lambda

numeric, the lambda parameter.

step

numeric, increment to decrease lambda.

atm_skew

numeric, ATM skew from data.

k_atm

a vector of numeric, range of log-strike to calculate ATM skew via lm.

ttm

numeric, time to expiration, with 1 representing 1 year (365 days).

otype

character, option type. Default: "c".

verbose

boolean, print debug message. Default: FALSE.

msg_prefix

character, command line message prefix. Default: "".

min_lambda

numeric, do not try lambda lower than this and return it. Default is 1.1.

Value

numeric, representing lambda.