Binomial_American_Greeks {greeks}

Computes the Greeks of an American call- or put-option with the Binomial options pricing model

Description

In contract to European Options, American options can be executed at any time until the expiration date. For more details on the definition of Greeks in general see Greeks. This functions computes Greeks of American put- and call options in the binomial option pricing model (see (Hull, 2022)).

Usage

Binomial_American_Greeks(
  initial_price = 100,
  exercise_price = 100,
  r = 0,
  time_to_maturity = 1,
  volatility = 0.3,
  dividend_yield = 0,
  payoff = "call",
  greek = c("fair_value", "delta", "vega", "theta", "rho", "epsilon", "gamma"),
  steps = 1000,
  eps = 1/1e+05
)

Arguments

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.

volatility

• volatility of the underlying asset.

dividend_yield

• dividend yield.

payoff

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

greek

• the Greek to be calculated.

steps

• the number of integration steps.

eps

• the step size for the finite difference method to calculate theta, vega, rho and epsilon

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

Greeks_UI for an interactive visualization

Examples

Binomial_American_Greeks(initial_price = 100, exercise_price = 100,
r = 0, time_to_maturity = 1, volatility = 0.3, dividend_yield = 0,
payoff = "call", greek = c("fair_value", "delta", "vega", "theta", "rho",
"epsilon", "gamma"), steps = 20)