deriva2.java

import static com.lambder.deriva.Deriva.*;

public class Formulas {

  public static Expression black(final boolean isCall) {

    // Logistic aproximation of Cumulated Standard Normal Distribution
    // 1/( e^(-0.07056 * x^3 - 1.5976*x) + 1)
    Expression N =  div(1.0,
        add(
            exp(
                sub(
                    mul(
                        -0.07056,
                        pow('x', 3)),
                    mul(-1.5976, 'x'))),
            1.0));

    // ( F/K+T*σ^2/2 ) / σ*sqrt(T)
    Expression d1 = div(
        add(
            div('F', 'K'),
            mul(div(sq("sigma"), 2.0), 'T')),
        mul("sigma", sqrt('T')));

    // ( F/K-T*σ^2/2 ) / σ*sqrt(T)
    Expression d2 = div(
        sub(
            div('F', 'K'),
            mul(div(sq("sigma"), 2.0), 'T')),
        mul("sigma", sqrt('T')));

    // e^(-r*T) * ( F*N(d1)-K*N(d2) )
    Expression call = mul(
        exp(neg(mul('r', 'T'))),
        sub(
            mul('F', N.bind('x', d1)),
            mul('K', N.bind('x', d2))));

    // e^(-r*T) * ( F*N(-d2)-K*N(-d1) )
    Expression put = mul(
        exp(neg(mul('r', 'T'))),
        sub(
            mul('F', N.bind('x', neg(d2))),
            mul('K', N.bind('x', neg(d1)))));

    return isCall ? call : put;    
  }

  // usage
  public static void main(String[] args) {
    // lets fix timeToExpiry to 0.523 and get only strike, forward and lognormalVol sensitivities
    Expression blackModel = black(true).bind('T', 0.523);
    Function1 fun = d(blackModel, 'F', 'K', 'r').function('F', 'K', 'r');
    fun.execute(12.3, 14.3, 0.03);
    fun.execute(12.3, 11.0, 0.03);
    fun.execute(12.3, 11.0, 0.02);
  }
}