Malliavin_European_Greeks {greeks}

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

• the 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). 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")