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from cmath import exp, pi
 
def fft(x):
    N = len(x)
    if N <= 1: return x
    even = fft(x[0::2])
    odd =  fft(x[1::2])
    T= [exp(-2j*pi*k/N)*odd[k] for k in range(N//2)]
    return [even[k] + T[k] for k in range(N//2)] + \
           [even[k] - T[k] for k in range(N//2)]
 
print( ' '.join("%5.3f" % abs(f) 
                for f in fft([1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0])) )

Code: Alles auswählen

import math
import numpy as np
import matplotlib.pylab as plt 
from math import *
import time
from scipy.fftpack import fft, ifft

N=32

l=[]
l2 =[]
for i in range(0,N):
    x=2*i
    y= np.sin(2*x)
    l.append(y)
    l2.append(x)

dx = l2[1]-l2[0]    
dw = 2*np.pi / (dx*N)

a=np.fft.fft(l) * dx 

b=np.fft.ifft(a) * dw


print (l)
print (a)
print (b)
    

Code: Alles auswählen

import math
import numpy as np
import matplotlib.pylab as plt
from math import *
import time
from scipy.fftpack import fft, ifft

N=32

l=[]
l2 =[]
for i in range(0,N):
    x=-N/2*2+2*i
    l.append(x)
    
al=np.array(l)    
y= np.sin(2*al)
yfft=fft(y)
bl=ifft(yfft)  

print (y)
print (yfft)    
print (bl)

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plt.figure()
plt.plot(l2, l)
plt.show()

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x = np.linspace(0, 1, 1000, endpoint=False)
y = np.sin(2*np.pi * x)
plt.figure()
plt.plot(x,y)
plt.show()

Code: Alles auswählen

import math
import numpy as np
import matplotlib.pylab as plt 
from math import *
import time
from scipy.fftpack import fft, ifft
start_time = time.clock()

# Definition od the option variables

r = -0.0032
S = 64.97

# ln (S)
s= np.log(S)

# Maturity
T = 81/365

vw =[]
# Number of Inputs. Equals the number of samples in the angular frequency space. Must be a power of 2 for FFT.
N = 4096

# Setting the angular frequency interval (spacing size)
dw = 0.25

# dw implies the following intervall dk in the log-strike space 
dk = 2*np.pi / (N*dw)

logK = []
K = []

# Set dumping parameter
a = 1

# Set Model parameter ----------------------------------------------------------------------------------------------------------- 

# sigma
vola = 0.2725523671

# -------------------------------------------------------------------------------------------------------------------------------

# phi, characteristic function (CF) of the chosen Lévy process. TO APPLY FFT FOR OTHER lÉVY PROCESSES JUST CHANGE THE CF (phi) below
def phi(w):
    return np.exp(1j*(s+(r-0.5*vola**2)*T)*w-(vola**2*T*w**2*0.5))

    # Fills the input array with N discrete values of the CF
for i in range(0, N):
 # discrete angular frequencies values w     
 wi = i*dw  
 vw.append(wi) 
 logstrikes = -(N/2) * dk + i*dk  
 logK.append(logstrikes)
 strike = np.exp(logK[i])
 K.append(strike)

w = np.array(vw)
 
g = (np.exp(-r*T)*phi(w-(a+1)*1j))/((a**2)+a-w**2+(1j*(2*a+1)*w))
fg = ifft(g)

alogK = np.array(logK)


C= (np.exp(-a*alogK)/(2*np.pi)) * (fg)


plt.plot(K[2048:2800], (C[2048:2800]))

#plt.plot(K[:2900], logK[:2900])
# calculates the computation time   
time = time.clock() - start_time