The O operator takes a vector of implied volatility \(\sigma_1(k)\)
and transforms them to a vector of normalized option prices.
The V operator takes a vector of normalized option prices and transforms
them to a vector of implied volatility \(\sigma_1(k)\).
If ttm is provided, \(\sigma_1(k)\) will be divided by square root of 2 ttm and yield Black-Scholes implied volatility.
The U operator calculates the log-slope of the option prices.
The op_VL_quartic operator is the quartic composite of V x OGF, assuming epsilon and rho are deposited in the ecld object.
The RN parameter for OGF is not available here. It is always assumed to be FALSE.
ecld.op_V(
L,
k,
otype = "c",
ttm = NaN,
rho = 0,
stop.on.na = FALSE,
use.mc = TRUE
)ecld.op_O(sigma1, k, otype = "c", rho = 0)
ecld.op_U_lag(L, k, sd, n = 2)
ecld.op_VL_quartic(
object,
k,
otype = "c",
ttm = NaN,
stop.on.na = FALSE,
use.mc = TRUE
)
numeric, a vector of normalized local option prices
numeric, a vector of log-strike
character, specifying option type:
c (default) or p.
numeric, time to expiration (maturity), measured by fraction of year. If specified, V operator will adjust \(\sigma_1(k)\) to Black-Scholes implied volatility. Default is NaN.
numeric, specify the shift in the global mu.
logical, to stop if fails to find solution. Default is to use NaN and not stop.
logical, to use mclapply, or else just use for loop.
Default is TRUE.
For loop option is typically for debugging.
numeric, a vector of implied volatility (without T)
numeric, the stdev of the distribution. Instead, if an ecld or ecd object is provided, the stdev will be calculated from it.
numeric, number of lags in ecld.op_U_lag.
an object of ecld class created from ecld.quartic.
This object contains the full quartic lambda model spec in order
to be used in ecld.op_VL_quartic
a numeric vector