When I simulate a stock's price path using geometric brownian motion I am sometimes able to get a pretty good forecast that fits the real values very well. But if I run the simulation again, the results are different. This is probably due to the random process of brownian motion.
Is there a way to run the same simulation (the one that fit the actual values well) over and over again without getting different results?
This is good when you are actually trading. Say for example you can run a test on some past data and then compare it with the real values to see if the model performed well or not. If it did, then you can use the same model for a future forecast in which you are going to buy and/or sell. But if the results are different on every simulation, then if you wish to do future forecast, you won't be able to test it with real data, since you are forecasting the future for which there is no data.
Here is my code. Half the time fits the data pretty, the other half not so.
#from __future__ import division
from random import gauss
from math import exp, sqrt
from matplotlib import pyplot as plt
import pandas as pd
import numpy as np
def generate_asset_price(S,v,r,T):
return S * exp((mu - 0.5 * v**2) * T + v * sqrt(T) * gauss(0,1.0))
#or dt instead of T
# return S * exp((mu - 0.5 * v**2) * T + v * sqrt(T) * gauss(0,1.0))
S0 = 12.2 # underlying price
v = 0.114764067
mu = -0.002773523
dt = 0.01 # 1 day
T = 20
n = int(20) # number of steps
S_path=[]
S=S0 # starting price
for i in xrange(1,n+1):
S_t = generate_asset_price(S,v,mu,dt)
S= S_t
S_path.append(S_t)
