Implied_Volatility {greeks}

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 = 1e-06,
  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")