Class AsianOption

java.lang.Object

com.quantfinlib.pricing.AsianOption

public final class AsianOption
extends Object

ASIAN (average-price) options — the corporate hedger's option: paying off on the AVERAGE of n fixings instead of one closing print kills both the expiry-day manipulation incentive and most of the vol (an average is smoother than its endpoints), which is why commodity and FX hedging programs default to them. Two averages, two methods:

• Geometric average — exact. A product of lognormals is lognormal, so the geometric Asian has a Black-Scholes-style closed form (Kemna-Vorst 1990, discrete-fixing version). For n fixings equally spaced at t_i = i T / n (last fixing AT expiry):

           E[ln G]   = ln S + (r - q - vol^2/2) * T (n+1)/(2n)
           Var[ln G] = vol^2 * T * (n+1)(2n+1)/(6 n^2)
         

  and the price is the Black-76 form on the lognormal G: discount E[G] N(d1) - K N(d2). As n grows, Var goes to vol^2 T / 3 — continuous averaging cuts the variance to a THIRD; at n = 1 both moments collapse to the terminal price and the formula IS vanilla Black-Scholes (tested exact).
• Arithmetic average — Turnbull-Wakeman (1991) moment matching. A sum of lognormals is not lognormal and has no closed form; TW computes the arithmetic average's first two moments EXACTLY under GBM,

           M1 = (S/n) sum_i e^{g t_i}                          g = r - q
           M2 = (S/n)^2 sum_i sum_j e^{g(t_i + t_j) + vol^2 min(t_i, t_j)}
         

  then prices Black-76 style on the lognormal with those moments (Var[ln A] = ln(M2/M1^2)). The approximation error is the distance of the true density from lognormal — small at practical vols, growing with vol^2 T; the moments themselves are exact. The double sum is O(n^2): fine for real fixing schedules (n ≤ a few hundred), not a Monte Carlo replacement for n in the tens of thousands.

AM-GM guarantees A >= G pathwise, so an arithmetic CALL is always worth at least the geometric call (tested) — the geometric price is the standard control variate for Monte Carlo on the arithmetic. Rates and vol are annualized and continuously compounded; carry is the dividend/foreign yield exactly as BlackScholes. Fixings strictly after inception (t_1 = T/n > 0): a seasoned Asian with fixings already struck is a payoff on the REMAINING average plus a known cash amount — decompose it before calling. Research lane.

Method Summary

Modifier and Type	Method	Description
static double	arithmeticPrice(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears, int averagingPoints)	Arithmetic-average Asian price via Turnbull-Wakeman two-moment lognormal matching (see class doc; O(n^2) in the fixing count).
static double	geometricPrice(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears, int averagingPoints)	Exact discrete geometric-average Asian price (Kemna-Vorst).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

geometricPrice

public static double geometricPrice(BlackScholes.OptionType type,
 double spot,
 double strike,
 double rate,
 double carry,
 double vol,
 double timeYears,
 int averagingPoints)

Exact discrete geometric-average Asian price (Kemna-Vorst).

Parameters:

averagingPoints - number of equally spaced fixings n ≥ 1 at t_i = i T / n; n = 1 is vanilla BS

arithmeticPrice

public static double arithmeticPrice(BlackScholes.OptionType type,
 double spot,
 double strike,
 double rate,
 double carry,
 double vol,
 double timeYears,
 int averagingPoints)

Arithmetic-average Asian price via Turnbull-Wakeman two-moment lognormal matching (see class doc; O(n^2) in the fixing count).