Good evening,

I try to implement the libor market model 1 factor to price caplet 1-years 10 years but something is wrong with the results. The first caplets' prices are quite close to the ones provided by Black but after Three years prices begin to differ significantly. I checked everything and i still can't find the problem. If anyone can help, it would be very nice. Thanks in advance.



Sub Question2()

Dim Strike As Double, Notional As Double, M As Long, maturite As Long, IRate As Double, spread As Double
spread = Range("B47")
Notional = Range("B48")
IRate = Range("B49")
M = Range("B50")
maturite = Range("B52")


Dim dt As Double, t As Long, sigma As Double
Dim F() As Double, vol() As Double, r() As Double, delta() As Double
Dim cap(1 To 10) As Double
ReDim vol(1 To 2, 0 To maturite - 1)
ReDim delta(0 To maturite)
ReDim F(0 To maturite, 0 To maturite)
ReDim r(1 To maturite, 1 To M)


For i = 0 To maturite - 1
vol(1, i) = Range("volatilite").Cells(i + 1)
vol(2, i) = Range("volatilite2").Cells(i + 1)
Next

For i = 0 To maturite
delta(i) = Range("delta").Cells(i + 1)
Next


For K = 0 To maturite
F(0, K) = IRate
Next

Rnd -1
Randomize seed

For j = 1 To M

For t = 1 To maturite

For i = t To maturite

Sum = (delta(t) * F(t - 1, t) * (vol(1, 0) * vol(1, i - t) + vol(2, 0) * vol(2, i - t))) / (1 + delta(t) * F(t - 1, t))
For s = t + 1 To i
Sum = Sum + (delta(s) * F(t - 1, s) * (vol(1, s - t) * vol(1, i - t) + vol(2, s - t) * vol(2, i - t))) / (1 + delta(s) * F(t - 1, s))
Next
F(t, i) = F(t - 1, i) * Exp((Sum - ((vol(1, i - t) * vol(1, i - t) + vol(2, i - t) * vol(2, i - t)) / 2) * delta(t - 1) + vol(1, i - t) * (delta(t - 1) ^ (0.5)) * Gauss() + vol(2, i - t) * (delta(t - 1) ^ 0.5) * Gauss()))
Next

discount = 1 + delta(0) * F(0, 0)
For D = 1 To t
discount = discount * (1 + delta(D) * F(D, D))
Next
r(t, j) = (Notional * delta(t) * Application.WorksheetFunction.Max(F(t, t) - F(t - 1, t - 1) - spread, 0)) / discount
Next

Next




For j = 1 To maturite

cap(j) = r(j, 1)
For i = 2 To M
cap(j) = cap(j) + r(j, i)
Next
cap(j) = cap(j) / M
Range("F" & 69 + j) = cap(j)

Dim var() As Double
ReDim var(1 To M)
For s = 1 To M
var(s) = r(j, s)
Next
Range("G" & 69 + j) = Application.WorksheetFunction.StDev(var) / (M ^ 0.5)



Next


















End Sub

Je sais que

To calculate caplet price by MC simulation, the easiest way is to simulate in forward measure.
eg., following file calculates option price in LMM using forward measure : Caplet Pricing by Monte Carlo simulation in Libor market model

Hope it helps

----------------
Please support Barsana eye camp

Thank you so much for your help. There is just one thing i don't understand in your program. Why are you using OriginalF(i) when computing drift sum and not F(i)? The formula i have uses F(i-1)... to compute F(i).

Thanks again