price_kemna_vorst_geometric: Kemna-Vorst Geometric Average Asian Option

In AsianOption: Asian Option Pricing with Price Impact

Kemna-Vorst Geometric Average Asian Option

Description

Calculates the price of a geometric average Asian call option using the closed-form analytical solution from Kemna & Vorst (1990). This is the standard benchmark implementation WITHOUT price impact.

Usage

price_kemna_vorst_geometric(S0, K, r, sigma, T0, T_mat, option_type = "call")

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. Gross risk-free interest rate per period (e.g., 1.05 for 5 Must be positive.
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.
option_type	Character. Type of option: "call" (default) or "put".

Details

The geometric average at maturity is defined as:

G_T = \exp\left(\frac{1}{T-T_0} \int_{T_0}^{T} \log(S(\tau)) d\tau\right)

For the discrete case with n+1 observations:

G_T = \left(\prod_{i=0}^{n} S(T_i)\right)^{1/(n+1)}

The closed-form solution for a call option is:

C = S_0 e^{d^*} N(d) - K N(d - \sigma_G\sqrt{T-T_0})

where:

d^* = \frac{1}{2}(r - \frac{\sigma^2}{6})(T - T_0)

d = \frac{\log(S_0/K) + \frac{1}{2}(r + \frac{\sigma^2}{6})(T-T_0)}{\sigma\sqrt{(T-T_0)/3}}

and N(\cdot) is the cumulative standard normal distribution function.

Value

Numeric. The analytical price of the geometric average Asian option.

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_geometric(
  S0 = 100, K = 100, r = 0.05, sigma = 0.2,
  T0 = 0, T_mat = 1, option_type = "call"
)

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