# -*- coding: utf-8 -*-
"""
Created on Thu Apr  8 13:52:28 2021

@author: turinici
"""

# %matplotlib auto
import numpy as np
import matplotlib.pyplot as plt


T=1.0
N=255
M=100 # nombre de scenarios
dt = T/N
W0=0

timerange = np.linspace(0,T,N+1,endpoint=True)
timerange=timerange[:,None]
dW= np.sqrt(dt)*np.random.randn(N,M)

W=np.zeros((N+1,M)) 
W[0,:]=W0
W[1:,:]=W0+np.cumsum(dW,0)

S0=100.
mu=0.1
sigma=0.25
taux_r=0.05

def st(mu,sigma,t,wt):
    return np.exp((mu-sigma**2/2.)*t + sigma*wt)

St = st(mu,sigma,timerange,W)*S0
plt.subplot(2,2,1)
plt.plot(timerange,W)
plt.title('Brownien')

plt.subplot(2,2,2)
plt.plot(timerange,St)
plt.title('St')

plt.subplot(2,2,3)
plt.hist(St[-1,:],50)
plt.title('hist de St')