Malliavin_Asian_Greeks {greeks}R Documentation

This function calculates the fair value of an European option by with the Malliavin Monte Carlo Method in the Black Scholes model.

Description

This function calculates the fair value of an European option by with the Malliavin Monte Carlo Method in the Black Scholes model.

Usage

Malliavin_Asian_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", "rho", "vega", "theta", "gamma"),
  model = "black_scholes",
  lambda = 0.2,
  alpha = 0.3,
  jump_distribution = function(n) stats::rt(n, df = 3),
  steps = round(time_to_maturity * 252),
  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.

volatility
  • volatility of the underlying asset.

dividend_yield
  • dividend yield.

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

greek
  • the Greek to be calculated.

model
  • the model to be chosen in ("black_scholes", "jump_diffusion")

lambda
  • the lambda of the Poisson process in the jump-diffusion model

alpha
  • the alpha in the jump-diffusion model influences the jump size

jump_distribution
  • the distribution of the jumps, choose a function which generates random numbers with the desired distribution

steps
  • the number of integration steps.

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.

Examples

Malliavin_Asian_Greeks(initial_price = 110, exercise_price = 100,
r = 0.02, time_to_maturity = 4.5, dividend_yield = 0.015, volatility = 0.22,
greek = c("fair_value", "delta", "rho"), payoff = "put")


[Package greeks version 0.2.0 Index]