Malliavin_Geometric_Asian_Greeks: Computes the Greeks of a geometric Asian option with the...

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

Computes the Greeks of a geometric Asian option with the Malliavin Monte Carlo Method in the Black Scholes- or Jump diffusion model

Description

In contrast to Asian options (see Malliavin_Asian_Greeks), geometric Asian options evaluate the geometric average \exp \left( \frac{1}{T} \int_0^T \ln S_t dt \right), where S_t is the price of the underlying asset at time t and T is the time-to-maturity of the option (see

en.wikipedia.org/wiki/Asian_option#European_Asian_call_and_put_options_with_geometric_averaging). For more details on the definition of Greeks see Greeks, and for a description of the Malliavin Monte Carlo Method for Greeks see for example (Hudde & Rüschendorf, 2023).

Usage

Malliavin_Geometric_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, can also be a vector
exercise_price	strike price of the option, can also be a vector
r	risk-free interest rate
time_to_maturity	time to maturity in years
volatility	volatility of the underlying asset
dividend_yield	dividend yield
payoff	the payoff function, either a string in ("call", "put", "digital_call", "digital_put"), or a function
greek	Greeks to be calculated in c("fair_value", "delta", "rho", "vega", "theta", "gamma)
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.

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_Geometric_Asian_Greeks for exact and fast computation in the Black Scholes model and for put- and call payoff functions

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")

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