python-Mcmc

 1 from time import time
 2 from math import exp,sqrt,log
 3 from random import gauss,seed
 4 seed(20000)
 5 t0 = time()
 6 
 7 S0 = 100
 8 K = 105
 9 T = 1.0
10 r = 0.05
11 sigma = 0.2
12 M = 50
13 dt = T / M
14 I = 250000
15 
16 S = []
17 for i in range(I):
18     path = []
19     for t in range(M + 1):
20         if(t == 0):
21             path.append(S0)
22         else:
23             z = gauss(0.0,1.0)
24             St = path[t-1] * exp((r - 0.5 * sigma ** 2) * dt + sigma * sqrt(dt) * z)
25             path.append(St)
26     S.append(path)
27 
28 C0 = exp(-r * T) * sum([max(path[-1]-K,0) for path in S]) / I
29 
30 tpy = time() - t0
31 print "European Option Vlue %7.3f" % C0
32 print "Duration in Seconds %7.3f" % tpy

 1 import math
 2 import numpy as np
 3 from time import time
 4 
 5 np.random.seed(20000)
 6 t0 = time()
 7 
 8 S0 = 100
 9 K = 105
10 T = 1.0
11 r = 0.05
12 sigma = 0.2
13 M = 50
14 dt = T / M
15 I = 250000
16 
17 S = np.zeros((M+1,I))
18 S[0] = S0
19 for t in range(1,M+1):
20     z = np.random.standard_normal(I)
21     S[t] = S[t-1] * np.exp((r - 0.5 * sigma ** 2) * dt + sigma * math.sqrt(dt) * z)
22 
23 C0 = math.exp(-r * T) * np.sum(np.maximum(S[-1]-K,0)) / I
24 
25 tpy = time() - t0
26 print "European Option Vlue %7.3f" % C0
27 print "Duration in Seconds %7.3f" % tpy

 1 import math
 2 from numpy import *
 3 from time import time
 4 
 5 random.seed(20000)
 6 t0 = time()
 7 
 8 S0 = 100
 9 K = 105
10 T = 1.0
11 r = 0.05
12 sigma = 0.2
13 M = 50
14 dt = T / M
15 I = 250000
16 
17 S = S0 * exp(cumsum((r - 0.5 * sigma ** 2) * dt + sigma * math.sqrt(dt) * random.standard_normal((M+1,I)), axis=0))
18 S[0] = S0
19 
20 print maximum(S[-1]-K,0)
21 
22 C0 = math.exp(-r * T) * sum(maximum(S[-1]-K,0)) / I
23 
24 tpy = time() - t0
25 print "European Option Vlue %7.3f" % C0
26 print "Duration in Seconds %7.3f" % tpy