simu_micro_heston.py

import numpy as np
import matplotlib.pyplot as plt
from math import e, pow
from util import LinkedList

mu_ = 0.1
beta = 1.1
Lambd = 1
K2 = 1
K1 = 1 + beta/K2
phi = []
maxlen = 11
def init(m, T):
    a_T = 1-Lambd/T
    N, lambd, dN, mu, phi = np.array([[100.],[0.]]), np.zeros((2,1)), LinkedList(np.zeros((2,1)),maxlen), np.ones((2,1))*m, []
    for t in range (maxlen):
        phi.append(PHI(t))
    return N, lambd, dN, mu, phi

def phi_1(t):
    return pow(e,-K1*t)

def phi_2(t):
    return pow(e, -K2*t)

def PHI(t):
    return np.array([[phi_1(t), beta*phi_2(t)],[phi_2(t), phi_1(t) + (beta-1)*phi_2(t)]])

def integr(t, dN, phi):
    res = np.zeros((2,1))
    dnlist = dN.getValues()
    if t<maxlen:
        for s in range(t):
            dn = np.reshape(dnlist[s],(2,1))
            #print (t-s)
            res += np.dot(phi[t-s],dn)
    else:
        for s in range(t-(maxlen-1), t):
            dn = np.reshape(dnlist[s-t+(maxlen -1)],(2,1))
            res += np.dot(phi[t-s],dn)
    return res

def evolue(lambd):
    x = np.random.random(2)
    dn = np.zeros((2,1))
    if (x[0] <= lambd[0,0]):
        dn[0,0] = 1
    if (x[1] <= lambd[1,0]):
        dn[1,0] = 1
    return dn

def simul(T,m):
    N, lambd, dN, mu, phi= init(m, T)
    P = [100]
    for t in range(T):
        lambd = mu + integr(t-1, dN, phi)
        dn =evolue(lambd)
        dN.addLast(dn)
        N += dn
        P.append(N[0,0] - N[1,0])
    #print (lambd)
    return P

def figure(T):
    t = np.arange(T)
    m =0
    for i in range (5):
        p = simul(T**2,mu_)
        P = [1/T*p[t*T] for t in range(T)]
        #m+= np.mean(P)
        plt.plot(t,P)
    m/=10
    #print (m)
    plt.title("Heston, h = %d, mu = %s, beta = %s, Lambda = %s, K1 = %s, K2 = %s, a_T = %s" %(T, mu_, beta, Lambd, K1, K2, 1-Lambd/T))
    plt.show()

figure(1000)
#for i in range (30):
#    print (i, phi_1(i), phi_2(i))