Package 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 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 Details

    • 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