CBOE_F_0: Calculate the theoretical at-the-money forward \mjseqnF_0...

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

Calculate the theoretical at-the-money forward \mjseqnF_0 from the CBOE VIX calculation. \loadmathjax

Description

Following the VIX whitepaper this function calculates \mjseqnF_0 as:

\mjsdeqn

F_0 := Strike Price + e^RT (Call Price - Put Price)

The variable \mjseqnR is the risk-free-rate (in decimal) for the corresponding time-to-maturity \mjseqnT (in years). The \mjseqnStrike Price, \mjseqnCall Price and \mjseqnPut Price are those where the absolute difference of the latter two is smallest.

Usage

CBOE_F_0(option_quotes, R, maturity)

Arguments

option_quotes	A data.table or "nest" of option quotes with three columns: K (numeric) - strike price in ascending order c (numeric) - call option price p (numeric) - put option price
R	numeric scalar giving the risk-free rate \mjseqnR corresponding to the maturity \mjseqnT in decimal
maturity	numeric scalar giving the time to maturity \mjseqnT in years

Value

Returns a numeric scalar, giving the theoretical at-the-money forward \mjseqnF_0

Examples

library(R.MFIV)

nest <- option_dataset$option_quotes[[1]]

CBOE_F_0(option_quotes = nest,
         R = 0.005,
         maturity = 0.07)

m-g-h/R.MFIV documentation built on June 13, 2025, 10:39 a.m.