Binomial European Options Pricing Model - vba

Question

I created a program, using VBA, to calculate the European Call option price, as follows:
Private Sub CallPrice_Click()
Dim K As Single
Dim So As Single
Dim r As Single
Dim T As Single
Dim sigma As Single
Dim u As Single
Dim d As Single
Dim p As Single
Dim CP As Single
Dim M As Single
Dim S As Single
Dim CB As Double
Dim n As Integer
Dim i As Integer
K = Cells(2, 2)
So = Cells(3, 2)
r = Cells(4, 2)
T = Cells(5, 2)
sigma = Cells(6, 2)
n = Cells(7, 2)
u = Exp(sigma * Sqr(T / n))
d = 1 / u
p = (Exp(r * T / n) - d) / (u - d)
CP = 0
For i = 0 To n Step 1
M = WorksheetFunction.Max(So * (u ^ i) * d ^ (n - i) - K, 0)
CB = WorksheetFunction.Combin(n, i)
S = M * CB * (p ^ n) * (1 - p) ^ (n - i)
CP = CP + S
Next i
Cells(9, 2) = CP / (1 + r) ^ n
End Sub
Here is the layout of the spreadsheet:
When I ran the program, the error occurred.
Could someone here explain what is wrong in my program and how to fix it?

Answer 1

Is your equation for S correct? It seems like it should be:
S = M * CB * (p ^ i) ...
instead of
S = M * CB * (p ^ n) ...
If your equation is indeed wrong, then you can use BINOMDIST instead of COMBIN, because by definition:
Binom_Dist(i, n, p, False) = (p ^ i) * (1 - p) ^ (n - i) * Combin(n, i)
So your code would be:
S = M * WorksheetFunction.Binom_Dist(i, n, p, False)
instead of
CB = WorksheetFunction.Combin(n, i)
S = M * CB * (p ^ n) * (1 - p) ^ (n - i)
BINOMDIST is not as sensitive to large n, i.

Answer 2

You are getting an overflow error. If you check on a work sheet:
COMBIN(5000, 161) = 3.3E+307
COMBIN(5000, 162) = #NUM!
COMBIN(5000, 4838) = #NUM!
COMBIN(5000, 4839) = 3.3E+307
Remember that the number of combinations increases exponentially up until the halfway point in which it will start to go down at an inverse rate.