price_kemna_vorst_arithmetic: Kemna-Vorst Arithmetic Average Asian Option

In AsianOption: Asian Option Pricing with Price Impact

Kemna-Vorst Arithmetic Average Asian Option

Description

Calculates the price of an arithmetic average Asian option using Monte Carlo simulation with variance reduction via the geometric average control variate. This implements the Kemna & Vorst (1990) method WITHOUT price impact.

Usage

price_kemna_vorst_arithmetic(
  S0,
  K,
  r,
  sigma,
  T0,
  T_mat,
  n,
  M = 10000,
  option_type = "call",
  use_control_variate = TRUE,
  seed = NULL,
  return_diagnostics = FALSE
)

Arguments

S0	Numeric. Initial stock price at time T0 (start of averaging period). Must be positive.
K	Numeric. Strike price. Must be positive.
r	Numeric. Continuously compounded risk-free rate (e.g., 0.05 for 5%). Use log(r_gross) to convert from gross rate.
sigma	Numeric. Volatility (annualized standard deviation). Must be non-negative.
T0	Numeric. Start time of averaging period. Must be non-negative.
T_mat	Numeric. Maturity time. Must be greater than T0.
n	Integer. Number of averaging points (observations). Must be positive.
M	Integer. Number of Monte Carlo simulations. Default is 10000. Larger values give more accurate results but take longer.
option_type	Character. Type of option: "call" (default) or "put".
use_control_variate	Logical. If TRUE (default), uses the geometric average as a control variate for variance reduction. This dramatically improves accuracy.
seed	Integer. Random seed for reproducibility. Default is NULL (no seed).
return_diagnostics	Logical. If TRUE, returns additional diagnostic information including confidence intervals, correlation, and variance reduction factor. Default is FALSE.

Value

If return_diagnostics = FALSE, returns a numeric value (the estimated option price). If return_diagnostics = TRUE, returns a list with components:

price

Estimated option price

std_error

Standard error of the estimate

lower_ci

Lower 95% confidence interval

upper_ci

Upper 95% confidence interval

geometric_price

Analytical geometric average price (control variate)

correlation

Correlation between arithmetic and geometric payoffs

variance_reduction_factor

Ratio of variances (with/without control)

n_simulations

Number of Monte Carlo simulations used

n_steps

Number of time steps in each simulation

References

Kemna, A.G.Z. and Vorst, A.C.F. (1990). "A Pricing Method for Options Based on Average Asset Values." Journal of Banking and Finance, 14, 113-129.

Examples

price_kemna_vorst_arithmetic(
  S0 = 100, K = 100, r = 0.05, sigma = 0.2,
  T0 = 0, T_mat = 1, n = 50, M = 10000
)

AsianOption documentation built on Dec. 23, 2025, 1:08 a.m.