# -*- coding: utf-8 -*-
"""
Weak EM scheme for Ornstein-Uhlenbeck, EM scheme for log normal.
@author: turinici
"""

import numpy as np
import matplotlib.pyplot as plt
T,N=1,500
h=T/N
M=1000
trange=np.linspace(0,T,N+1,endpoint=True)
theta=1
mu=10
sigma=3.


print('weak Euler Maruyama for Ornstein-Uhlenbeck')
X=np.zeros((N+1,M))

for ii in range(N):
    xi=2*np.random.binomial(1,0.5,M)-1
    X[ii+1,:] =X[ii,:]+ theta*(mu-X[ii,:])*h+np.sqrt(h)*sigma*xi
    
plt.hist(X[-1,:])

plt.plot(X)


print('Black-Scholes with Euler-Maruyama')

mu=0.25
sigma=0.15
X=np.zeros((N+1,M))
X[0,:]=100

for ii in range(N):
    
    X[ii+1,:] =X[ii,:]+ mu*X[ii,:]*h+np.sqrt(h)*sigma*X[ii,:]*np.random.randn(M)

plt.hist(X[-1,:])
plt.plot(X)