View source: R/JandT_smoothing.R
JandT_2007_smoothing_method | R Documentation |
Intrapolates and extrapolates the option_quotes over the strike price range using the Jiang & Tian (2007) smoothing method. The given quotes are transformed into Black & Scholes implied volatilities, on which intra/extrapolation takes place.
JandT_2007_smoothing_method( option_quotes, K_0, price, R, maturity, F_0, tail_length = 15, flat_tails = T, increment = "min" )
option_quotes |
A
|
K_0 |
|
price |
|
R |
|
maturity |
|
F_0 |
|
tail_length |
|
flat_tails |
|
increment |
The increment is at least 0.5, unless a numeric value is provided. |
Inside the given range of strike prices, (natural) cubic spline intrapolation takes place.
The tails are extrapolated linearly. For flat
extrapolation, the "outer-most"
implied volatility is used, for sloped
extrapolation the slope of the two
"outer-most" implied volatilities is used.
After intra/extrapolation, the implied volatilities are transformed back into option prices via Black&Scholes, i.e. out-of-the-money puts and calls.
Jiang & Tian (2007) define the range and increment of the strike prices in \mjseqnSD
units. This \mjseqnSD is the Black & Scholes implied volatility of the at-the-money
option. As an example, the increment recommended by Jiang & Tian (2007) is \mjseqn0.35
units: \mjseqnSD \cdot \sqrtmaturity \cdot price \cdot 0.35. The range is calculated
accordingly as \mjseqnSD \cdot \sqrtmaturity \cdot price \cdot tail_length
.
Returns a data.table
of intra- and extrapolated option quotes with the
following columns:
K (numeric
) - evenly spaced strike price in ascending order
Q (numeric
) - OTM option price
doi: 10.1093/rfs/hhi027 Jiang & Tian (2005) - The Model-Free Implied Volatility and Its Information Content
doi: 10.3905/jod.2007.681813 Jiang & Tian (2007) - Extracting Model-Free Volatility from Option Prices: An Examination of the VIX Index
library(R.MFIV) ## LOAD EXAMPLE OPTION_QUOTES nest <- option_dataset$option_quotes[[1]] ## EXTRAPOLATE DATA JandT_2007_smoothing_method(option_quotes = nest, maturity = 0.06644802, K_0 = 147, R = 0.008769736, F_0 = 147.5697, price = 147.39)
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