#
# Call Option Pricing with Circular Convolution (Simple)
# 06_fou/call_convolution.py
#
# (c) Dr. Yves J. Hilpisch
# Derivatives Analytics with Python
#
import math
import numpy as np
from convolution import revnp, convolution
# Parameter Definitions
M = 4 # number of time steps
dt = 1.0 / M # length of time interval
r = 0.05 # constant short rate
C = [49.18246976, 22.14027582, 0, 0, 0] # call payoff at maturity
q = 0.537808372 # martingale probability
qv = np.array([q, 1 - q, 0, 0, 0]) # probabilitiy vector filled with zeros
# Calculation
V = np.zeros((M + 1, M + 1), dtype=np.float)
V[M] = C
for t in range(M - 1, -1, -1):
V[t] = convolution(V[t + 1], revnp(qv)) * math.exp(-r * dt)
print "Value of the Call Option %8.3f" % V[0, 0]
# Call Option Pricing with Circular Convolution (General)
import numpy as np
from convolution import revnp, convolution
from parameters import *
# Parameter Adjustments
M = 3 #numberoftimesteps
dt, df, u, d, q = get_binomial_parameters(M)
# Array Generation for Stock Prices
mu = np.arange(M + 1)
mu = np.resize(mu, (M + 1, M + 1))
md = np.transpose(mu)
mu = u**(mu - md)
md = d**md
S = S0 * mu * md
# Valuation
V = np.maximum(S - K, 0)
qv = np.zeros((M + 1), dtype=np.float)
qv[0] = q
qv[1] = 1 - q
for t in range(M - 1, -1, -1):
V[:, t] = convolution(V[:, t + 1], revnp(qv)) * df
print("Value of the Call Option %8.3f" % V[0, 0])
import numpy as np from numpy.fft import fft, ifft from convolution import revnp from parameters import * # Parmeter Adjustments M = 3 # number of time steps dt, df, u, d, q = get_binomial_parameters(M) # Array Generation for Stock Prices mu = np.arange(M + 1) mu = np.resize(mu, (M + 1, M + 1)) md = np.transpose(mu) mu = u ** (mu - md) md = d ** md S = S0 * mu * md # Valuation by fft CT = np.maximum(S[:, -1] - K, 0) qv = np.zeros(M + 1, dtype=np.float) qv[0] = q qv[1] = 1 - q C0_a = fft(math.exp(-r * T) * ifft(CT) * ((M + 1) * ifft(revnp(qv))) ** M) C0_b = fft(math.exp(-r * T) * ifft(CT) * fft(qv) ** M) C0_c = ifft(math.exp(-r * T) * fft(CT) * fft(revnp(qv)) ** M) # Results Outpu print "Value of European option is %8.3f" % np.real(C0_a[0]) print "Value of European option is %8.3f" % np.real(C0_b[0]) print "Value of European option is %8.3f" % np.real(C0_c[0])
import math
import numpy as np
from numpy.fft import fft, ifft
from convolution import revnp
from parameters import *
# Parmeter Adjustments
M = 3 # number of time steps
dt, df, u, d, q = get_binomial_parameters(M)
# Array Generation for Stock Prices
mu = np.arange(M + 1)
mu = np.resize(mu, (M + 1, M + 1))
md = np.transpose(mu)
mu = u ** (mu - md)
md = d ** md
S = S0 * mu * md
# Valuation by fft
CT = np.maximum(S[:, -1] - K, 0)
qv = np.zeros(M + 1, dtype=np.float)
qv[0] = q
qv[1] = 1 - q
C0_a = fft(math.exp(-r * T) * ifft(CT) * ((M + 1) * ifft(revnp(qv))) ** M)
C0_b = fft(math.exp(-r * T) * ifft(CT) * fft(qv) ** M)
C0_c = ifft(math.exp(-r * T) * fft(CT) * fft(revnp(qv)) ** M)
# Results Outpu
print("Value of European option is %8.3f" % np.real(C0_a[0]))
print("Value of European option is %8.3f" % np.real(C0_b[0]))
print("Value of European option is %8.3f" % np.real(C0_c[0]))
# 06_fou/call_convolution_general.py
#
# (c) Dr. Yves J. Hilpisch
# Derivatives Analytics with Python
#
import numpy as np
from convolution import revnp, convolution
from parameters import *
# Parmeter Adjustments
M = 3 # number of time steps
dt, df, u, d, q = get_binomial_parameters(M)
# Array Generation for Stock Prices
mu = np.arange(M + 1)
mu = np.resize(mu, (M + 1, M + 1))
md = np.transpose(mu)
mu = u ** (mu - md)
md = d ** md
S = S0 * mu * md
# Valuation
V = np.maximum(S - K, 0)
qv = np.zeros((M + 1), dtype=np.float)
qv[0] = q
qv[1] = 1 - q
for t in range(M - 1, -1, -1):
V[:, t] = convolution(V[:, t + 1], revnp(qv)) * df
print("Value of the Call Option %8.3f" % V[0, 0])