com.illumon.numerics.derivatives

Class BlackScholes

java.lang.Object

com.illumon.numerics.derivatives.BlackScholes

public class BlackScholes
extends Object

A generalized Black-Scholes model for European options.

Method Summary

Modifier and Type	Method and Description
static double	carryRho(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes carryRho (first order partial derivative of option price with respect to cost-of-carry).
static double	charm(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes charm (first order partial derivative of Delta with respect to time to expiry).
static double	delta(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes delta (first order partial derivative of option price with respect to stock price).
static double	driftlessTheta(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes driftlessTheta (theta assuing the risk free rate and the cost of carry are zero).
static double	gamma(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes gamma (second order partial derivative of option price with respect to stock price).
static double	gammaP(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes percentage gamma (first order partial derivative of delta with respect to ln(stock price)).
static double	impliedVolBisect(double P, Boolean isCall, double S, double X, double T, double r, double b) Generalized Black-Scholes implied vol fitter using a bisection algorithm.
static double	impliedVolBisect(double P, Boolean isCall, double S, double X, double T, double r, double b, double eps, int maxIters) Generalized Black-Scholes implied vol fitter using a bisection algorithm.
static double	impliedVolNewton(double P, Boolean isCall, double S, double X, double T, double r, double b) Generalized Black-Scholes implied vol fitter using a newton algorithm.
static double	impliedVolNewton(double P, Boolean isCall, double S, double X, double T, double r, double b, double eps, int maxIters) Generalized Black-Scholes implied vol fitter using a newton algorithm.
static double	impliedVolNewtonP(double P, Boolean isCall, double S, double X, double T, double r, double b) Generalized Black-Scholes implied vol fitter using a newton algorithm based on log(vol).
static double	impliedVolNewtonP(double P, Boolean isCall, double S, double X, double T, double r, double b, double eps, int maxIters) Generalized Black-Scholes implied vol fitter using a newton algorithm based on log(vol).
static double	price(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes option price.
static double	rho(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes rho (first order partial derivative of option price with respect to risk-free rate).
static double	strikeDelta(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes strikeDelta (first order partial derivative of option price with respect to strike price).
static double	strikeFromDeltaBisect(double delta, Boolean isCall, double S, double T, double r, double b, double v) Finds the Generalized Black-Scholes strike from the delta.
static double	strikeFromDeltaBisect(double delta, Boolean isCall, double S, double T, double r, double b, double v, double eps, int maxIters) Finds the Generalized Black-Scholes strike from the delta.
static double	theta(boolean isCall, double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes theta (first order partial derivative of option price with respect to time to expiry).
static double	vega(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes vega (first order partial derivative of option price with respect to volatility).
static double	vegaBleed(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes vegaBleed (first order partial derivative of Vega with respect to time to expiry).
static double	vegaP(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes percentage vega (first order partial derivative of vega with respect to ln(volatility)).
static double	vomma(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes vomma (second order partial derivative of option price with respect to volatility).
static double	vommaP(double S, double X, double T, double r, double b, double v) Computes the generalized Black-Scholes percentage vomma (first order partial derivative of Vega with respect to ln(volatility)).

Methods inherited from class java.lang.Object

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

Method Detail

price

public static double price(boolean isCall,
                           double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes option price.

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

delta

public static double delta(boolean isCall,
                           double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes delta (first order partial derivative of option price with respect to stock price).

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option delta

gamma

public static double gamma(double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes gamma (second order partial derivative of option price with respect to stock price).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

gammaP

public static double gammaP(double S,
                            double X,
                            double T,
                            double r,
                            double b,
                            double v)

Computes the generalized Black-Scholes percentage gamma (first order partial derivative of delta with respect to ln(stock price)).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

vega

public static double vega(double S,
                          double X,
                          double T,
                          double r,
                          double b,
                          double v)

Computes the generalized Black-Scholes vega (first order partial derivative of option price with respect to volatility).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

vegaP

public static double vegaP(double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes percentage vega (first order partial derivative of vega with respect to ln(volatility)).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

vomma

public static double vomma(double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes vomma (second order partial derivative of option price with respect to volatility).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

vommaP

public static double vommaP(double S,
                            double X,
                            double T,
                            double r,
                            double b,
                            double v)

Computes the generalized Black-Scholes percentage vomma (first order partial derivative of Vega with respect to ln(volatility)).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

vegaBleed

public static double vegaBleed(double S,
                               double X,
                               double T,
                               double r,
                               double b,
                               double v)

Computes the generalized Black-Scholes vegaBleed (first order partial derivative of Vega with respect to time to expiry).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

charm

public static double charm(boolean isCall,
                           double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes charm (first order partial derivative of Delta with respect to time to expiry).

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

theta

public static double theta(boolean isCall,
                           double S,
                           double X,
                           double T,
                           double r,
                           double b,
                           double v)

Computes the generalized Black-Scholes theta (first order partial derivative of option price with respect to time to expiry).

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

driftlessTheta

public static double driftlessTheta(double S,
                                    double X,
                                    double T,
                                    double r,
                                    double b,
                                    double v)

Computes the generalized Black-Scholes driftlessTheta (theta assuing the risk free rate and the cost of carry are zero).

Parameters:

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

rho

public static double rho(boolean isCall,
                         double S,
                         double X,
                         double T,
                         double r,
                         double b,
                         double v)

Computes the generalized Black-Scholes rho (first order partial derivative of option price with respect to risk-free rate).

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

carryRho

public static double carryRho(boolean isCall,
                              double S,
                              double X,
                              double T,
                              double r,
                              double b,
                              double v)

Computes the generalized Black-Scholes carryRho (first order partial derivative of option price with respect to cost-of-carry).

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

strikeDelta

public static double strikeDelta(boolean isCall,
                                 double S,
                                 double X,
                                 double T,
                                 double r,
                                 double b,
                                 double v)

Computes the generalized Black-Scholes strikeDelta (first order partial derivative of option price with respect to strike price).

Parameters:

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

theoretical option price

impliedVolBisect

public static double impliedVolBisect(double P,
                                      Boolean isCall,
                                      double S,
                                      double X,
                                      double T,
                                      double r,
                                      double b)

Generalized Black-Scholes implied vol fitter using a bisection algorithm.

Parameters:

P - option price

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

Returns:

implied volatility

impliedVolBisect

public static double impliedVolBisect(double P,
                                      Boolean isCall,
                                      double S,
                                      double X,
                                      double T,
                                      double r,
                                      double b,
                                      double eps,
                                      int maxIters)

Generalized Black-Scholes implied vol fitter using a bisection algorithm.

Parameters:

P - option price

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

eps - volatility convergence tolerance

maxIters - maximum number of optimization iterations

Returns:

implied volatility

impliedVolNewton

public static double impliedVolNewton(double P,
                                      Boolean isCall,
                                      double S,
                                      double X,
                                      double T,
                                      double r,
                                      double b)

Generalized Black-Scholes implied vol fitter using a newton algorithm.

Parameters:

P - option price

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

Returns:

implied volatility

impliedVolNewton

public static double impliedVolNewton(double P,
                                      Boolean isCall,
                                      double S,
                                      double X,
                                      double T,
                                      double r,
                                      double b,
                                      double eps,
                                      int maxIters)

Generalized Black-Scholes implied vol fitter using a newton algorithm.

Parameters:

P - option price

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

eps - volatility convergence tolerance

maxIters - maximum number of optimization iterations

Returns:

implied volatility

impliedVolNewtonP

public static double impliedVolNewtonP(double P,
                                       Boolean isCall,
                                       double S,
                                       double X,
                                       double T,
                                       double r,
                                       double b)

Generalized Black-Scholes implied vol fitter using a newton algorithm based on log(vol).

Parameters:

P - option price

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

Returns:

implied volatility

impliedVolNewtonP

public static double impliedVolNewtonP(double P,
                                       Boolean isCall,
                                       double S,
                                       double X,
                                       double T,
                                       double r,
                                       double b,
                                       double eps,
                                       int maxIters)

Generalized Black-Scholes implied vol fitter using a newton algorithm based on log(vol).

Parameters:

P - option price

isCall - true for call; false for put.

S - underlying stock price

X - strike price

T - years to expiry

r - risk-free rate

b - cost-of-carry

eps - volatility convergence tolerance

maxIters - maximum number of optimization iterations

Returns:

implied volatility

strikeFromDeltaBisect

public static double strikeFromDeltaBisect(double delta,
                                           Boolean isCall,
                                           double S,
                                           double T,
                                           double r,
                                           double b,
                                           double v)

Finds the Generalized Black-Scholes strike from the delta.

Parameters:

delta - delta

isCall - true for call; false for put.

S - underlying stock price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

Returns:

strike associated with the delta

strikeFromDeltaBisect

public static double strikeFromDeltaBisect(double delta,
                                           Boolean isCall,
                                           double S,
                                           double T,
                                           double r,
                                           double b,
                                           double v,
                                           double eps,
                                           int maxIters)

Finds the Generalized Black-Scholes strike from the delta.

Parameters:

delta - delta

isCall - true for call; false for put.

S - underlying stock price

T - years to expiry

r - risk-free rate

b - cost-of-carry

v - volatility

eps - volatility convergence tolerance

maxIters - maximum number of optimization iterations

Returns:

strike associated with the delta