Function outperf_delta_math(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the delta of an outperformance option
v = Sqr(v1 ^ 2 + v2 ^ 2 - 2 * rho * v1 * v2)
d1 = (Application.Ln(S2 / S1) + (q1 - q2 + 0.5 * v ^ 2) * t) / (v * Sqr(t))
d2 = d1 - v * Sqr(t)
zwi = (S2 * Exp(-q2 * t) * phi(d1) - S1 * Exp(-q1 * t) * phi(d2)) / (v * Sqr(t))
If take_12 = 1 Then
    outperf_delta_math = -(zwi + S1 * Exp(-q1 * t) * Gauss(d2)) / S1
    ElseIf take_12 = 2 Then
    outperf_delta_math = (zwi + S2 * Exp(-q2 * t) * Gauss(d1)) / S2
    Else: outperf_delta_math = "False"
End If
End Function


Function outperf_gamma_math(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the gamma of an outperformance option
v = Sqr(v1 ^ 2 + v2 ^ 2 - 2 * rho * v1 * v2)
d1 = (Application.Ln(S2 / S1) + (q1 - q2 + 0.5 * v ^ 2) * t) / (v * Sqr(t))
d2 = d1 - v * Sqr(t)
g = (S1 * Exp(-q1 * t) * phi(d2) * (1 + d2 / (v * Sqr(t))) + S2 * Exp(-q2 * t) * phi(d1) * (1 - d1 / (v * Sqr(t)))) / (v * Sqr(t))
If take_12 = 11 Then
    outperf_gamma_math = g / (S1 ^ 2)
    ElseIf take_12 = 12 Then
    outperf_gamma_math = -g / (S1 * S2)
    ElseIf take_12 = 21 Then
    outperf_gamma_math = -g / (S1 * S2)
    ElseIf take_12 = 22 Then
    outperf_gamma_math = g / (S2 ^ 2)
    Else: outperf_gamma_math = "False"
End If
End Function

Function outperf_delta(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the delta of an outperformance option
plus = 0.01
op = outperf(S1, S2, t, q1, q2, v1, v2, rho)
op1 = outperf(S1 + plus, S2, t, q1, q2, v1, v2, rho)
op2 = outperf(S1, S2 + plus, t, q1, q2, v1, v2, rho)
del1 = (op1 - op) / plus
del2 = (op2 - op) / plus
If take_12 = 1 Then
    outperf_delta = del1
    ElseIf take_12 = 2 Then
    outperf_delta = del2
    Else: outperf_delta = "False"
End If
End Function


Function outperf_gamma(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the gamma of an outperformance option
plus = 0.01
op1 = outperf_delta(S1, S2, t, q1, q2, v1, v2, rho, 1)
op2 = outperf_delta(S1, S2, t, q1, q2, v1, v2, rho, 2)
op11 = outperf_delta(S1 + plus, S2, t, q1, q2, v1, v2, rho, 1)
op12 = outperf_delta(S1 + plus, S2, t, q1, q2, v1, v2, rho, 2)
op21 = outperf_delta(S1, S2 + plus, t, q1, q2, v1, v2, rho, 1)
op22 = outperf_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
    outperf_gamma = gam11
    ElseIf take_12 = 12 Then
    outperf_gamma = gam12
    ElseIf take_12 = 21 Then
    outperf_gamma = gam21
    ElseIf take_12 = 22 Then
    outperf_gamma = gam22
    Else: outperf_gamma = "False"
End If
End Function


Function outperf_vega(S1, S2, t, q1, q2, v1, v2, rho, take_12)
' Delivers the vega of an outperformance option
plus = 0.01
op = outperf(S1, S2, t, q1, q2, v1, v2, rho)
op1 = outperf(S1, S2, t, q1, q2, v1 + plus, v2, rho)
op2 = outperf(S1, S2, t, q1, q2, v1, v2 + plus, rho)
veg1 = (op1 - op)
veg2 = (op2 - op)
If take_12 = 1 Then
    outperf_vega = veg1
    ElseIf take_12 = 2 Then
    outperf_vega = veg2
    Else: outperf_vega = "False"
End If
End Function


Function outperf_theta(S1, S2, t, q1, q2, v1, v2, rho)
' Delivers the theta of an outperformance option
plus = 1 / 360
op = outperf(S1, S2, t, q1, q2, v1, v2, rho)
op1 = outperf(S1, S2, t + plus, q1, q2, v1, v2, rho)
outperf_theta = -op1 + op
End Function