type mismatch error in VBA, where is the mistake - vba

Question

Hey I have no idea why I get an error "run time error 13 type mismatch". Thats my code and the place where I get an error:
EDIT: That is my code:
Function payoff(S_T, K, CallPut As String)
If CallPut = "call" Then
omega = 1
Else: omega = -1
End If
payoff = WorksheetFunction.Max(omega * (S_T - K), 0)
End Function
Function BS_trajektoria(S_0 As Double, T As Double, r As Double, q As Double, sigma As Double, N As Long) As Double()
Randomize
Dim S() As Double
Dim delta_t As Double
Dim i As Long
ReDim S(N)
S(0) = S_0
delta_t = T / N
For i = 1 To N
S(i) = S(i - 1) * Exp((r - q - 0.5 * sigma ^ 2) * delta_t + sigma * delta_t ^ 0.5 * Application.NormSInv(Rnd))
Next i
BS_trajektoria = S
End Function
Function barrier_MC(S_0 As Double, K As Double, T As Double, r As Double, q As Double, sigma As Double, _
B As Double, N As Long, num_of_sim As Long, CallPut As String, BarType As String) As Double
Randomize
Dim max_value As Double
Dim suma_wyplat As Double
Dim wyplata As Double
Dim i As Long
Dim S() As Double
suma_wyplat = 0
If (BarType = "DO" Or BarType = "DI") And B > S_0 Then
MsgBox "Too high barrier!"
Exit Function
ElseIf (BarType = "UO" Or BarType = "UI") And B < S_0 Then
MsgBox "Too low barrier!"
Exit Function
End If
With WorksheetFunction
For i = 1 To num_of_sim
S = BS_trajektoria(S_0, T, r, q, sigma, N)
max_value = .Max(S)
If max_value >= B Then
wyplata = 0
Else
wyplata = payoff(S(N), K, CallPut)
End If
suma_wyplat = suma_wyplat + wyplata
Next i
End With
barrier_MC = Exp(-r * T) * suma_wyplat / num_of_sim
End Function
Sub test3()
MsgBox barrier_MC(100, 100, 1, 0.05, 0.02, 0.2, 120, 1000, 1000000, "call", "UO")
End Sub
Anyone know where is the problem? For smaller value of N and num_of_sim everything works fine, the problem is when I use bigger values for these variables.

Answer 1

If you declare a new Double variable called rand and modify the main loop so that it looks like:
For i = 1 To N
rand = Rnd
S(i) = S(i - 1) * Exp((r - q - 0.5 * sigma ^ 2) * delta_t + sigma * delta_t ^ 0.5 * Application.NormSInv(rand))
Next i
you will see that the problem always happens when rand = 0. Why it throws that particular error is a bit of a mystery, but it is what it is. As a fix, what you could do is to keep the code as modified above with the following twist:
For i = 1 To N
rand = Rnd
If rand = 0 Then rand = 0.0000001
S(i) = S(i - 1) * Exp((r - q - 0.5 * sigma ^ 2) * delta_t + sigma * delta_t ^ 0.5 * Application.NormSInv(rand))
Next i
Then the code will run without error. It is still somewhat slow, but optimizing it (if possible) would be for a different question.