Class BlackScholes

java.lang.Object

com.quantfinlib.pricing.BlackScholes

public final class BlackScholes
extends Object

Black-Scholes-Merton option pricing and Greeks with a continuous carry yield q: set q to the dividend yield for equities or the foreign interest rate for FX (Garman-Kohlhagen). All rates and volatility are annualized; theta is per year; vega/rho are per 1.00 change.

With vol <= 0 every function returns the deterministic limit instead of dividing by σ√T: delta is the discounted in-the-money indicator on the forward (one half at F = K), gamma is 0, vega is 0 except exactly at the forward, theta and rho are the derivatives of the discounted forward intrinsic value.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	BlackScholes.Greeks	Full Greek set for one option.
static enum	BlackScholes.OptionType

Method Summary

Modifier and Type	Method	Description
static double	delta(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears)
static double	gamma(double spot, double strike, double rate, double carry, double vol, double timeYears)
static BlackScholes.Greeks	greeks(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears)
static double	impliedVol(BlackScholes.OptionType type, double marketPrice, double spot, double strike, double rate, double carry, double timeYears)	Implied volatility from a market price, through ImpliedVolatility.black(BlackScholes.OptionType, double, double, double, double) on the forward F = S e^{(r-q)T} and the undiscounted price.
static double	intrinsic(BlackScholes.OptionType type, double spot, double strike)
static double	price(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears)
static double	rho(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears)	Per 1.00 change in the domestic rate.
static double	theta(BlackScholes.OptionType type, double spot, double strike, double rate, double carry, double vol, double timeYears)	Per year (divide by 365 for per-calendar-day).
static double	vega(double spot, double strike, double rate, double carry, double vol, double timeYears)	Per 1.00 change in volatility (divide by 100 for per-vol-point).

Methods inherited from class Object

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

Method Details

price

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

delta

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

gamma

public static double gamma(double spot,
 double strike,
 double rate,
 double carry,
 double vol,
 double timeYears)

vega

public static double vega(double spot,
 double strike,
 double rate,
 double carry,
 double vol,
 double timeYears)

Per 1.00 change in volatility (divide by 100 for per-vol-point).

theta

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

Per year (divide by 365 for per-calendar-day).

rho

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

Per 1.00 change in the domestic rate.

greeks

public static BlackScholes.Greeks greeks(BlackScholes.OptionType type,
 double spot,
 double strike,
 double rate,
 double carry,
 double vol,
 double timeYears)

impliedVol

public static double impliedVol(BlackScholes.OptionType type,
 double marketPrice,
 double spot,
 double strike,
 double rate,
 double carry,
 double timeYears)

Implied volatility from a market price, through ImpliedVolatility.black(BlackScholes.OptionType, double, double, double, double) on the forward F = S e^{(r-q)T} and the undiscounted price. Accurate to a few ulps of σ wherever the price itself carries information, including deep wings and very short or long expiries. Returns NaN when the price is outside the attainable range (below intrinsic, or at or above the discounted zero-strike bound) and 0 when it equals intrinsic exactly.

intrinsic

public static double intrinsic(BlackScholes.OptionType type,
 double spot,
 double strike)