Malliavin_European_Greeks: Computes the Greeks of a European option with the Malliavin...

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

Computes the Greeks of a European option with the Malliavin Monte Carlo Method in the Black Scholes model

Description

For details on the definition of Greeks see Greeks. For a description of Malliavin Monte Carlo Methods for Greeks see for example (Hudde & Rüschendorf, 2023).

Usage

Malliavin_European_Greeks(
  initial_price = 100,
  exercise_price = 100,
  r = 0,
  time_to_maturity = 1,
  volatility = 0.3,
  payoff = "call",
  greek = c("fair_value", "delta", "vega", "theta", "rho", "gamma"),
  model = "Black Scholes",
  paths = 10000,
  seed = 1,
  antithetic = FALSE
)

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 in years
volatility	volatility of the underlying asset
payoff	the payoff function, either a string in ("call", "put", "cash_or_nothing_call", "cash_or_nothing_call", "asset_or_nothing_call", "asset_or_nothing_put"), or a function
greek	Greeks to be calculated in ("fair_value", "delta", "vega", "theta", "rho", "gamma")
model	the model to be chosen
paths	the number of simulated paths
seed	the seed of the random number generator
antithetic	if TRUE, antithetic random numbers will be chosen to decrease variance

Value

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

References

Hudde, A., & Rüschendorf, L. (2023). European and Asian Greeks for Exponential Lévy Processes. Methodol Comput Appl Probab, 25 (39). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11009-023-10014-5")}

See Also

BS_European_Greeks for the exact and fast implementation for call-, put- and digital payoff functions

Examples

Malliavin_European_Greeks(initial_price = 110,
exercise_price = 100, r = 0.02, time_to_maturity = 4.5,
volatility = 0.22, greek = c("fair_value", "delta", "rho"), payoff = "put")

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