Implied_Volatility: Computes the implied volatility for various options via...

In anselmhudde/greeks: Sensitivities of Prices of Financial Options and Implied Volatilities

Computes the implied volatility for various options via Newton's method

Description

If the value of an option, and other (model)parameters like the risk-free interest rate, the time-to-maturity, and the dividend yield are known, the assumed volatility of the underlying asset, the implied volatility can be inferred. See Hull (2022).

Usage

Implied_Volatility(
  option_price,
  initial_price = 100,
  exercise_price = 100,
  r = 0,
  time_to_maturity = 1,
  dividend_yield = 0,
  model = "Black_Scholes",
  option_type = "European",
  payoff = "call",
  start_volatility = 0.3,
  precision = 0.000001,
  max_iter = 30
)

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 in years
dividend_yield	dividend yield
model	the model to be chosen
option_type	in c("European", "American", "Geometric Asian", "Asian", "Digital") - the type of option to be considered
payoff	in c("call", "put")
start_volatility	initial guess
precision	precision of the computation
max_iter	maximal number of iterations of the approximation

Value

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

References

Hull, J. C. (2022). Options, futures, and other derivatives (11th Edition). Pearson

See Also

BS_Implied_Volatility for the special case option_type = "European" and payoff in c("call", "put")

Examples

Implied_Volatility(15, r = 0.05, option_type = "Asian",
payoff = "call")

anselmhudde/greeks documentation built on April 14, 2025, 3:56 p.m.