python-Mcmc

Python pandas的效率比较：

from time import time
from math import exp,sqrt,log
from random import gauss,seed
seed(20000)
t0 = time()

S0 = 100
K = 105
T = 1.0
r = 0.05
sigma = 0.2
M = 50
dt = T / M
I = 250000

S = []
for i in range(I):
    path = []
    for t in range(M + 1):
        if(t == 0):
            path.append(S0)
        else:
            z = gauss(0.0,1.0)
            St = path[t-1] * exp((r - 0.5 * sigma ** 2) * dt + sigma * sqrt(dt) * z)
            path.append(St)
    S.append(path)

C0 = exp(-r * T) * sum([max(path[-1]-K,0) for path in S]) / I

tpy = time() - t0
print "European Option Vlue %7.3f" % C0
print "Duration in Seconds %7.3f" % tpy

引用numpy

import math
import numpy as np
from time import time

np.random.seed(20000)
t0 = time()

S0 = 100
K = 105
T = 1.0
r = 0.05
sigma = 0.2
M = 50
dt = T / M
I = 250000

S = np.zeros((M+1,I))
S[0] = S0
for t in range(1,M+1):
    z = np.random.standard_normal(I)
    S[t] = S[t-1] * np.exp((r - 0.5 * sigma ** 2) * dt + sigma * math.sqrt(dt) * z)

C0 = math.exp(-r * T) * np.sum(np.maximum(S[-1]-K,0)) / I

tpy = time() - t0
print "European Option Vlue %7.3f" % C0
print "Duration in Seconds %7.3f" % tpy

import math
from numpy import *
from time import time

random.seed(20000)
t0 = time()

S0 = 100
K = 105
T = 1.0
r = 0.05
sigma = 0.2
M = 50
dt = T / M
I = 250000

S = S0 * exp(cumsum((r - 0.5 * sigma ** 2) * dt + sigma * math.sqrt(dt) * random.standard_normal((M+1,I)), axis=0))
S[0] = S0

print maximum(S[-1]-K,0)

C0 = math.exp(-r * T) * sum(maximum(S[-1]-K,0)) / I

tpy = time() - t0
print "European Option Vlue %7.3f" % C0
print "Duration in Seconds %7.3f" % tpy