CBOE_sigma_sq: Calculate the CBOE VIX model free variance \mjseqn\sigma^2

In m-g-h/R.MFIV: Calculate Model Free Implied Volatility, i.e. the CBOE VIX from Option Quotes

Calculate the CBOE VIX model free variance \mjseqn\sigma^2

Description

This function performs the CBOE VIX model-free implied variance calculation according to the following formula from the 2019 VIX whitepaper: \loadmathjax \mjsdeqn\sigma^2 = \frac2T \left(\sum_i \frac\Delta K_iK_i^2 Q(K_i) e^rT \right) - \frac1T \left( \fracF_0K_0 - 1 \right)^2 It uses CBOE_delta_K internally to derive the weights \mjseqn\Delta K_i

Usage

CBOE_sigma_sq(sel_option_quotes, K_0, F_0, maturity, R)

Arguments

sel_option_quotes	A data.table or "nest" of option quotes as selected by CBOE_option_selection
K_0	numeric scalar, giving the theoretical at-the-money strike price (see CBOE_K_0)
F_0	numeric scalar, giving the theoretical at-the-money forward \mjseqnF_0 (see CBOE_F_0)
maturity	numeric scalar giving the time to maturity \mjseqnT in years
R	numeric scalar giving the risk-free rate \mjseqnR corresponding to the maturity \mjseqnT in decimal

Value

Returns a numeric scalar: the model-free implied volatility \mjseqn\sigma^2 as per the CBOE formula above.

Examples

library(R.MFIV)
nest <- CBOE_option_selection(option_dataset$option_quotes[[1]],
                              147)
CBOE_sigma_sq(sel_option_quotes = nest,
             maturity = 0.06644802,
             K_0 = 147,
             R = 0.008769736,
             F_0 = 147.5697)

m-g-h/R.MFIV documentation built on July 4, 2022, 3:35 a.m.