Function CTD_delta(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the delta of a cheapest to deliver option
plus = 0.01
op = CTD(S1, S2, t, q1, q2, v1, v2, rho)
op1 = CTD(S1 + plus, S2, t, q1, q2, v1, v2, rho)
op2 = CTD(S1, S2 + plus, t, q1, q2, v1, v2, rho)
del1 = (op1 - op) / plus
del2 = (op2 - op) / plus
If take_12 = 1 Then
    CTD_delta = del1
    ElseIf take_12 = 2 Then
    CTD_delta = del2
    Else: CTD_delta = "Falsh"
End If
End Function


Function CTD_gamma(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the gamma of a cheapest to deliver option
plus = 0.01
op1 = CTD_delta(S1, S2, t, q1, q2, v1, v2, rho, 1)
op2 = CTD_delta(S1, S2, t, q1, q2, v1, v2, rho, 2)
op11 = CTD_delta(S1 + plus, S2, t, q1, q2, v1, v2, rho, 1)
op12 = CTD_delta(S1 + plus, S2, t, q1, q2, v1, v2, rho, 2)
op21 = CTD_delta(S1, S2 + plus, t, q1, q2, v1, v2, rho, 1)
op22 = CTD_delta(S1, S2 + plus, t, q1, q2, v1, v2, rho, 2)
gam11 = (op11 - op1) / plus
gam12 = (op12 - op2) / plus
gam21 = (op21 - op1) / plus
gam22 = (op22 - op2) / plus
If take_12 = 11 Then
    CTD_gamma = gam11
    ElseIf take_12 = 12 Then
    CTD_gamma = gam12
    ElseIf take_12 = 21 Then
    CTD_gamma = gam21
    ElseIf take_12 = 22 Then
    CTD_gamma = gam22
    Else: CTD_gamma = "False"
End If
End Function


Function CTD_vega(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the vega of a cheapest to deliver option
plus = 0.01
op = CTD(S1, S2, t, q1, q2, v1, v2, rho)
op1 = CTD(S1, S2, t, q1, q2, v1 + plus, v2, rho)
op2 = CTD(S1, S2, t, q1, q2, v1, v2 + plus, rho)
veg1 = (op1 - op)
veg2 = (op2 - op)
If take_12 = 1 Then
    CTD_vega = veg1
    ElseIf take_12 = 2 Then
    CTD_vega = veg2
    Else: CTD_vega = "False"
End If
End Function


Function CTD_theta(S1, S2, t, q1, q2, v1, v2, rho)
' Delivers the theta of a cheapest to deliver option
plus = 1 / 360
op = CTD(S1, S2, t, q1, q2, v1, v2, rho)
op1 = CTD(S1, S2, t + plus, q1, q2, v1, v2, rho)
CTD_theta = -op1 + op
End Function