BS_Implied_Volatility {greeks}

Computes the implied volatility for European put- and call options in the Black Scholes model via Halley's method.

Description

For the definition of implied volatility see Implied_Volatility. BS_Implied_Volatility offers a very fast implementation for European put- and call options applying Halley's method (see

en.wikipedia.org/wiki/Halley%27s_method).

Usage

BS_Implied_Volatility(
  option_price,
  initial_price = 100,
  exercise_price = 100,
  r = 0,
  time_to_maturity = 1,
  dividend_yield = 0,
  payoff = "call",
  start_volatility = 0.3,
  precision = 1e-09
)

Arguments

option_price

• current price of the option

initial_price

• initial price of the underlying asset.

exercise_price

• strike price of the option.

r

• risk-free interest rate.

time_to_maturity

• time to maturity.

dividend_yield

• dividend yield.

payoff

• the payoff function, a string in ("call", "put").

start_volatility

• the volatility value to start the approximation

precision

• precision of the result

Value

Named vector containing the values of the Greeks specified in the parameter greek.

See Also

Implied_Volatility for American and Asian options, and for digital payoff functions

Examples

BS_Implied_Volatility(option_price = 27, initial_price = 100,
exercise_price = 100, r = 0.03, time_to_maturity = 5, dividend_yield = 0.015,
payoff = "call")