pricingModel.py

import numpy as np
import scipy.stats as ss
import time
def BinomialTree(type,S0, K, r, sigma, T, N=2000):
    #calculate delta T
    deltaT = np.divide(float(T), N)
    # up and down factor will be constant for the tree so we calculate outside the loop
    u = np.exp(sigma * np.sqrt(deltaT))
    d = np.divide(1.0, u)
    # Initialise our f_{i,j} tree with zeros
    fs = [[0.0 for j in xrange(i + 1)] for i in xrange(N + 1)]
    #store the tree in a triangular matrix
    #this is the closest to theory
    #no need for the stock tree
    #rates are fixed so the probability of up and down are fixed.
    #this is used to make sure the drift is the risk free rate
    a = np.exp(r * deltaT)
    p = np.divide(np.subtract(a, d), np.subtract(u, d) + np.finfo(float).eps)
    oneMinusP = 1.0 - p
 # Compute the leaves, f_{N, j}
    for j in xrange(i+1):
        if type =="C":
            fs[N][j] = max(S0 * np.power(u, j) * d**(N - j) - K, 0.0)
        elif type =="P":
            fs[N][j] = max(-S0 * np.power(u, j) * d**(N - j) + K, 0.0)
        else:
            print("Please select either C fo Call or P for Put.")
            return 0
 # calculate backward the option prices
    for i in xrange(N-1, -1, -1):
        for j in xrange(i + 1):
            fs[i][j] = np.exp(-r * deltaT) * (p * fs[i + 1][j + 1] + oneMinusP * fs[i + 1][j])
    return fs[0][0]

# set up values here
S0 = 37.72     # current value
K = 38         # target value
r= 0.024       # risk-free rate
sigma = 0.1037 # Volatility

expiring_days = 121.0 #remaining trading days


Otype='C'

print "S0\tstock price at time 0:", S0
print "K\tstrike price:", K
print "r\tcontinuously compounded risk-free rate:", r
print "sigma\tvolatility of the stock price per year:", sigma
# print "T\ttime to maturity in trading years:", T

price_result = []
for i in range(4):
    T = (expiring_days - 30 * i)/251.0
    price_result.append(BinomialTree(Otype,S0, K, r, sigma, T, 1500))

print(price_result)