' Calculates the probability of a black scholes options to go above a certain frontier.
Function phi(X As Double) As Double
    phi = 1 / Sqr(2 * Application.Pi()) * Exp(-X ^ 2 / 2)
End Function


Function fi(X As Double) As Double
    fi = 1 / Sqr(2 * Application.Pi()) * Exp(-X ^ 2 / 2)
End Function


Function Gauss(X As Double) As Double
    Gauss = Application.NormSDist(X)
End Function


Function d_1(S As Double, X As Double, t As Double, r As Double, q As Double, v As Double) As Double
' d1 result of the black-scholes formula
    d_1 = (Log(S / X) + (r - q + v ^ 2 / 2) * t) / (v * Sqr(t))
End Function


Function prob_above(S As Double, X As Double, t As Double, r As Double, q As Double, v As Double) As Double
' Calculates the probability above a given frontier
    Dim d1 As Double, d2 As Double
    d1 = d_1(S, X, t, r, q, v)
    d2 = d1 - v * Sqr(t)
    prob_above = Gauss(d2)
End Function