Public Function N(ByVal X As Double) As Double ' !*
    Dim ax, t, d, p As Double
    If X > 10 Then
        N = 1
    ElseIf X < -10 Then
        N = 0
    Else
        ax = Sqr(X * X)
        t = 1 / (1 + 0.2316419 * ax)
        d = 0.3989423 * Exp(-0.5 * X * X)
        p = d * t * ((((1.330274 * t - 1.821256) * _
        t + 1.781478) * t - 0.3565638) * t + 0.3193815)
        N = p
        If X > 0 Then N = 1 - p Else N = p
    End If
End Function

Public Function TTM(ByVal Today As Date, _
    ByVal Expiry As Date) As Double ' Time to maturity, years
    TTM = (Expiry - Today + 1) / 365
End Function

Public Function Discount(ByVal IRate As Double, _
    ByVal Today As Date, ByVal Expiry As Date) As Double
    Discount = Exp(-TTM(Today, Expiry) * IRate)
End Function

Public Function D1(ByVal Futures As Double, ByVal _
    Strike As Double, ByVal Today _
    As Date, ByVal Expiry As Date, ByVal StDev As Double) As Double
    D1 = (Log(Futures / Strike) + (StDev * StDev / 2) * _
    TTM(Today, Expiry)) / (StDev * Sqr(TTM(Today, Expiry)))
End Function

' Black-Scholes Futures Option Pricing Model
' European Call Option Price
Public Function EFC(ByVal IRate As Double, _
    ByVal Futures As Double, ByVal Strike As Double, _
    ByVal Today As Date, ByVal Expiry As Date, _
    ByVal StDev As Double) As Double
    Dim Dtmp, FunctTmp As Double
    Dtmp = D1(Futures, Strike, Today, Expiry, StDev)
    FunctTmp = Discount(IRate, Today, Expiry) * _
    (Futures * (N(Dtmp)) - Strike _
    * (N(Dtmp - StDev * Sqr(TTM(Today, Expiry)))))
    EFC = FunctTmp
End Function

' European Call Option Delta !**
Public Function EFCDelta(ByVal IRate As Double, _
    ByVal Futures As Double, ByVal Strike As Double, _
    ByVal Today As Date, ByVal Expiry As Date, _
    ByVal StDev As Double) As Double
    Dim Dtmp, FunctTmp As Double
    Dtmp = D1(Futures, Strike, Today, Expiry, StDev)
    EFCDelta = exp(-Sqr(TTM(Today, Expiry))*IRate)*N(Dtmp)
End Function