def compute_expectation_mc(qgy, num_sim, n_per_year):
n = qgy.n
sigma2 = []
sigma2_prime = []
dt = 1 / n_per_year
for i in range(1, n):
for j in range(n_per_year):
t = qgy.Tk[i - 1] + dt * (j + 1)
sigma2.append(qgy.inf_vol(t))
sigma2_prime.append(qgy.inf_vol_prime(t))
sigma2_prime = None
sigma_n = np.repeat(1, n_per_year * (n - 1))
sigma_n_prime = None #np.repeat(0, n_per_year * (n - 1))
phi_Tk = gen_phi_vec_list(qgy)
psi_Tk = gen_psi_matx_list(qgy)
#quasi monte carlo
permut_matrix = qgy.generate_permutation_matrix(num_sim,
(n - 1) * n_per_year)
sob_seq = qgy.generate_sobol_squence(num_sim, 3)
######################
np.random.seed(seed=12345)
ans = np.zeros(n)
for i in range(num_sim):
# use pesudo random number
[x_n, x_y1] = qgy.generate_two_correlated_gauss(
sigma_n, sigma2, qgy.rho_n_y1, (n - 1) * n_per_year,
1 / n_per_year, sigma_n_prime, sigma2_prime)
x_y2 = qgy.generate_one_gauss(sigma2, (n - 1) * n_per_year,
1 / n_per_year, sigma2_prime)
# use quasi random number
#[x_n, x_y1] = qgy.generate_two_correlated_quasi_gauss(sigma_n, sigma2, qgy.rho_n_y1, dt, i, permut_matrix, sob_seq, [1, 2])
#x_y2 = qgy.generate_one_quasi_gauss(sigma2, dt, i, permut_matrix, sob_seq, 0)
x_Tk_y1 = np.concatenate([[0], x_y1[n_per_year - 1::n_per_year]])
x_Tk_y2 = np.concatenate([[0], x_y2[n_per_year - 1::n_per_year]])
x_n_Tk = np.concatenate([[0], x_n[n_per_year - 1::n_per_year]])
one_path = np.zeros(n)
for j in range(len(x_Tk_y1)):
x_Tk = np.matrix([x_n_Tk[j], x_Tk_y1[j], x_Tk_y2[j]]).T
X_Tk = qgy.Xt(x_Tk, phi_Tk[j], psi_Tk[j])
one_path[j] = X_Tk
#plt.plot(qgy.Tk, one_path, 'g.')
ans += one_path
ans /= num_sim
ans[0] = 1
return ans
from Model.QgyModel import *
test = [10, 20, 40, 80, 160, 320]
num_sim = 10000
for num_per_year in test:
dt = 1 / num_per_year
qgy = QgyModel()
qgy.n_per_year = num_per_year
N = num_per_year * (qgy.n - 1)
sigma = np.repeat(1, N)
res = []
for i in range(num_sim):
one_path = qgy.generate_one_gauss(sigma, N, dt)
res.append(one_path[-1])
#plt.plot(one_path, 'g-')
#plt.show()
var = np.var(res)
mean = np.mean(res)
print("num_per_year = ", num_per_year, "mean = ", mean, ", var = ", var)
dt = 1 / qgy.n_per_year
for i in range(1, len(qgy.R_Tk_y)):
for j in range(qgy.n_per_year):
t = qgy.Tk[i - 1] + dt * (j + 1)
sigma2.append(qgy.inf_vol(t))
sigma2_prime.append(qgy.inf_vol_prime(t))
sigma_n = np.repeat(1, N)
sigma_n_prime = np.repeat(0, N)
t = np.linspace(1, qgy.Tk[-1], qgy.n_per_year * (qgy.n - 1))
dist = []
N = 100
for i in range(0, N):
[x_n,
x_y1] = qgy.generate_two_correlated_gauss(sigma_n, sigma2, qgy.rho_n_y1,
(qgy.n - 1) * qgy.n_per_year,
1 / qgy.n_per_year,
sigma_n_prime, sigma2_prime)
x_y2 = qgy.generate_one_gauss(sigma2, (qgy.n - 1) * qgy.n_per_year,
1 / qgy.n_per_year, sigma2_prime)
x_Tk_y1 = x_y1[::qgy.n_per_year]
x_Tk_y2 = x_y2[::qgy.n_per_year]
plt.subplot(1, 3, 1)
plt.plot(t, x_n, 'r')
plt.subplot(1, 3, 2)
plt.plot(t, x_y1, 'b')
plt.subplot(1, 3, 3)
plt.plot(t, x_y2, 'g')
plt.show()