JandT_2007_sigma_sq: Calculate the MFIV according to the Jiang & Tian (2007) paper

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

Calculate the MFIV according to the Jiang & Tian (2007) paper

Description

This function performs the model-free implied variance calculation according to the following formula from Jiang & Tian (2007): \loadmathjax \mjsdeqnV = \frac2T \exp(R T) (A + B) \mjsdeqnA = \sum_i \leq 0 \frac\Delta \hatK_i2 \left( \fracP^EX (\hatK_i, T)\hatK^2_i + \fracP^EX (\hatK_j, T)\hatK^2_j \right)

\mjsdeqn

B = \sum_i \leq 0 \frac\Delta \hatK_i2 \left( \fracC^EX (\hatK_i, T)\hatK^2_i + \fracC^EX (\hatK_j, T)\hatK^2_j \right) \mjsdeqn \Delta \hatK_i = \hatK_i - \hatK_j \mjsdeqnj = i-1

Usage

JandT_2007_sigma_sq(smooth_option_quotes, K_0, maturity, R)

Arguments

smooth_option_quotes	A data.table or "nest" of option quotes as returned from JandT_2007_smoothing_method
K_0	numeric scalar, giving the theoretical at-the-money strike price (see CBOE_K_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.

References

doi: 10.3905/jod.2007.681813 Jiang & Tian (2007) - Extracting Model-Free Volatility

Examples

library(R.MFIV)

## LOAD EXAMPLE OPTION_QUOTES
nest <- option_dataset$option_quotes[[1]]

## EXTRAPOLATE DATA
smooth_nest <- JandT_2007_smoothing_method(option_quotes = nest,
                                           maturity = 0.008953152,
                                           K_0 = 147,
                                           price = 147.39,
                                           R = 0.008325593,
                                           F_0 = 147.405)
## CALCULATE MFIV
sigma_sq <- JandT_2007_sigma_sq(smooth_option_quotes = smooth_nest,
                                K_0 = 147,
                                maturity = 0.008953152,
                                R = 0.008325593)

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