black76ImVo: black76ImVo

In OUKUN0705/black76IV: Black76 model

Description

black76ImVo returns the implied volatility based on black model, Black(1976). It employs Newton–Raphson method based on vega of the option.

Usage

black76ImVo(Ft, K, type, Time, r, optionPrice, sigma_ini = NULL,
  tol = 1e-10, maxiter = 1000)

Arguments

Ft	Future price. Numeric object.
K	Strike price. Numeric object.
type	Type of the European option, call(c) or put(p). String object.
Time	Time to maturity (in year). Numeric object.
r	Continousely compounded interest rate. Numeric object.
optionPrice	Observed market option premium. Numeric object.
sigma_ini	Initial value for iteration in the Newton-Raphson method. Numeric object or NULL(default). If no value is provided, the sigma which maximizes Vega is choosen.
tol	Error tolerance of the interation step.
maxiter	Maximum number of iteration.

Value

Calculated implied volatilited.

Examples

price <- black76(type = "C", Ft = 48.03, Time = 0.1423, K = 50,
                  sigma = 0.2, r = 0.03)
black76ImVo(type = "C", Ft = 48.03, Time = 0.1423, K = 50, sigma_ini = 1, r = 0.03,
            optionPrice = price[1], tol = 1e-10, maxiter = 20)

price <- black76(type = "C", Ft = 50, Time = 1, K = 62,
                  sigma = 0.342, r = 0.2186)
black76ImVo(type = "C", Ft = 50, Time = 1, K = 62, r = 0.2186,
            optionPrice = price[1], tol = 1e-10, maxiter = 20)

This example illustrates when the Time value (volatility) is too
small compared to intrinsic value (moneyness), the root finding is too
difficult due to the flat slope around the root (close to zero vega).
price <- black76(type = "C", Ft = 50, Time = 0.25, K = 26,
                 sigma = 0.1261, r = 0.2584)
black76ImVo(type = "C", Ft = 50, Time = 5, K = 26, r = 0.2584,
            optionPrice = price[1], tol = 1e-20, maxiter = 1000)
price <- black76(type = "C", Ft = 50, Time = 0.25, K = 26,
                 sigma = 0.1, r = 0.2584)
price <- black76(type = "C", Ft = 50, Time = 0.25, K = 26,
                 sigma = 0.3, r = 0.2584)

OUKUN0705/black76IV documentation built on May 7, 2019, 8:55 p.m.