Je ne parviens pas à matcher le prix d'options à barrières de type Call Up and In avec les formules de type BS et la méthode de MC.
Voyez vous mon erreur?
Cf fichier en attachment Cdt.
Ludovic
Code : Sélectionner et copier le code
Sub CUIPRICE()
Dim Barrierefranchise As Integer
GetData
Dim Stinit As Double
Stinit = St
Dim moyenneCUI As Double
Dim unif As Double
moyenneCUI = 0
If St < L Then
Dim Stplusdt As Double
Dim i As Long
Dim j As Long
For i = 1 To N
Barrierefranchise = 0
For j = partieentiere(t * 260) To partieentiere((M * 260))
Randomize
unif = Rnd
z = WorksheetFunction.Norm_Inv(unif, 0, 1)
Stplusdt = St * (1 + z * sigma * WorksheetFunction.Power((M - t) / 260, 0.5) + (r - div) * ((M - t) / 260))
St = Stplusdt
If Stplusdt > L Then
Barrierefranchise = 1
End If
Next
moyenneCUI = moyenneCUI + Barrierefranchise * partiepositive(St * Exp((r - div - 0.5 * WorksheetFunction.Power(sigma, 2)) * (M - t) + sigma * WorksheetFunction.Power(M - t, 0.5) * z) - K)
St = Stinit
Next
ElseIf St > L Then
moyenneCUI = 0
End If
Worksheets("Feuil1").Cells(17, 4) = Exp(-r * (M - t)) * moyenneCUI / N
End Sub
Code : Sélectionner et copier le code
Function CUIPRICE(St As Double, t As Double, K As Double, r As Double, M As Double, sigma As Double, L As Double) As Double
If St < L Then
If K > L Then
CUIPRICE = function1(1, St, div, M, r, sigma, t, K)
ElseIf K < L Then
CUIPRICE = function2(1, St, div, M, r, sigma, t, K, L) - function3(1, -1, St, div, M, r, sigma, t, K, L) + function4(1, -1, St, div, M, r, sigma, t, K, L)
End If
ElseIf St > L Then
CUIPRICE = 0
End If
End Function
Code : Sélectionner et copier le code
Function mu(r As Double, div As Double, sigma As Double) As Double
mu = r - div - 0.5 * WorksheetFunction.Power(sigma, 2)
End Function
Function eps(sigma As Double) As Double
eps = (mu(r, div, sigma) / WorksheetFunction.Power(sigma, 2)) + 1
End Function
Function x(St As Double, t As Double, M As Double, K As Double) As Double
x = (WorksheetFunction.Ln(St / K) / (sigma * WorksheetFunction.Power(M - t, 0.5))) + eps(sigma) * sigma * WorksheetFunction.Power((M - t), 0.5)
End Function
Function x1(St As Double, t As Double, M As Double, L As Double) As Double
x1 = (WorksheetFunction.Ln(St / L) / (sigma * WorksheetFunction.Power(M - t, 0.5))) + eps(sigma) * sigma * WorksheetFunction.Power((M - t), 0.5)
End Function
Function y(St As Double, t As Double, M As Double, L As Double) As Double
y = (WorksheetFunction.Ln(WorksheetFunction.Power(L, 2) / (St * K)) / (sigma * WorksheetFunction.Power(M - t, 0.5))) + eps(sigma) * sigma * WorksheetFunction.Power(M, 0.5)
End Function
Function y1(St As Double, t As Double, M As Double, L As Double) As Double
y1 = (WorksheetFunction.Ln(L / St) / (sigma * WorksheetFunction.Power(M - t, 0.5))) + eps(sigma) * sigma * WorksheetFunction.Power(M, 0.5)
End Function
Function function1(fi As Double, St As Double, div As Double, M As Double, r As Double, sigma As Double, t As Double, K As Double) As Double
function1 = fi * St * Exp(-div * (M - t)) * WorksheetFunction.Norm_Dist(fi * x(St, t, M, K), 0, 1, True) - fi * K * Exp(r * (M - t)) * WorksheetFunction.Norm_Dist(fi * x(St, t, M, K) - fi * sigma * WorksheetFunction.Power((M - t), 0.5), 0, 1, True)
End Function
Function function2(fi As Double, St As Double, div As Double, M As Double, r As Double, sigma As Double, t As Double, K As Double, L As Double) As Double
function2 = fi * St * Exp(-div * (M - t)) * WorksheetFunction.Norm_Dist(fi * x1(St, t, M, L), 0, 1, True) - fi * K * Exp(r * (M - t)) * WorksheetFunction.Norm_Dist(fi * x1(St, t, M, L) - fi * sigma * WorksheetFunction.Power((M - t), 0.5), 0, 1, True)
End Function
Function function3(fi As Double, nu As Double, St As Double, div As Double, M As Double, r As Double, sigma As Double, t As Double, K As Double, L As Double) As Double
function3 = fi * St * Exp(-div * (M - t)) * WorksheetFunction.Power((L / St), 2 * eps(sigma)) * WorksheetFunction.Norm_Dist(nu * y(St, t, M, L), 0, 1, True) - fi * K * Exp(r * (M - t)) * WorksheetFunction.Power((L / St), 2 * (eps(sigma) - 1)) * WorksheetFunction.Norm_Dist(nu * y(St, t, M, L) - nu * sigma * WorksheetFunction.Power((M - t), 0.5), 0, 1, True)
End Function
Function function4(fi As Double, nu As Double, St As Double, div As Double, M As Double, r As Double, sigma As Double, t As Double, K As Double, L As Double) As Double
function4 = fi * St * Exp(-div * (M - t)) * WorksheetFunction.Power((L / St), 2 * eps(sigma)) * WorksheetFunction.Norm_Dist(nu * y1(St, t, M, L), 0, 1, True) - fi * K * Exp(r * (M - t)) * WorksheetFunction.Power((L / St), 2 * (eps(sigma) - 1)) * WorksheetFunction.Norm_Dist(nu * y1(St, t, M, L) - nu * sigma * WorksheetFunction.Power((M - t), 0.5), 0, 1, True)
End Function
