excel - Recursion code in VBA

Question

I am trying to run this code to calculate Q(n) at different Tn in the Equation 16.4 in the attached picture.But its not giving me the correct output. I would appreciate any help. Note: delta1=delta2 =...deltan = dt=1 ( I have taken here ) and further divided S term by 10000 just because in the Equation it is in basis point i.e. 100th part of 1 %.

Function Bootstrap(S As Range, Z As Range, L As Double) As Double
Dim j As Integer
Dim a As Variant
Dim b As Variant
Dim n As Integer
Dim Q() As Double
Dim sum As Double
Dim P As Double
Dim dt As Double

n = Application.WorksheetFunction.Max(S.Columns.Count, Z.Columns.Count)
a = S.Value
b = Z.Value
dt = 1
sum = 0
ReDim Q(0 To n)
Q(0) = 1

For j = 1 To n - 1
    P = (b(1, j) * (L * Q(j - 1) - (L + dt * a(1, n) / 10000) * Q(j))) / (b(1, n) * (L + a(1, n) * dt / 10000)) + Q(n - 1) * L / (L + a(1, n) * dt / 10000)
    sum = sum + P
    Q(n) = sum
Next j

Bootstrap = sum
End Function

Answer 1

To solve a recursive function you can write it this way, for example

Function Factorial(n as long) as long
    If n = 1 Then
        Factorial = 1
    Else
        Factorial = n * Factorial(n-1)
    End If
End function

Yes, you can see For...Loop can also do the Factorial calculation, but in your case, its much easier to use recursive solution.

Besides Eq 16.4 is intentionally written as a recursive function. It is not written as a summation function because it is harder to do so. If given to you is a summation function, then you can apply the For...Loop solution.

Hope this helps.

EDIT

Function Q(n as long) as double

    If n = 1 Then
        Q = 5
    Else
        Q = Z * ( L * Q_t - (L + d * S) * Q(n-1) ) / ( Z * ( L + d * S ) )
    End If

End Function

Notice that the function Q keep calling itself in Q(n-1) when n>1. That is called recursive solution.

(Check the formula. I might copy it wrong)